NP-hardness of decoding quantum error-correction codes
Hsieh, Min-Hsiu; Le Gall, François
2011-05-01
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
NP-hardness of decoding quantum error-correction codes
International Nuclear Information System (INIS)
Hsieh, Min-Hsiu; Le Gall, Francois
2011-01-01
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
Neural network decoder for quantum error correcting codes
Krastanov, Stefan; Jiang, Liang
Artificial neural networks form a family of extremely powerful - albeit still poorly understood - tools used in anything from image and sound recognition through text generation to, in our case, decoding. We present a straightforward Recurrent Neural Network architecture capable of deducing the correcting procedure for a quantum error-correcting code from a set of repeated stabilizer measurements. We discuss the fault-tolerance of our scheme and the cost of training the neural network for a system of a realistic size. Such decoders are especially interesting when applied to codes, like the quantum LDPC codes, that lack known efficient decoding schemes.
Error-correction coding and decoding bounds, codes, decoders, analysis and applications
Tomlinson, Martin; Ambroze, Marcel A; Ahmed, Mohammed; Jibril, Mubarak
2017-01-01
This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of these codes. Part IV deals with decoders desi...
New decoding methods of interleaved burst error-correcting codes
Nakano, Y.; Kasahara, M.; Namekawa, T.
1983-04-01
A probabilistic method of single burst error correction, using the syndrome correlation of subcodes which constitute the interleaved code, is presented. This method makes it possible to realize a high capability of burst error correction with less decoding delay. By generalizing this method it is possible to obtain probabilistic method of multiple (m-fold) burst error correction. After estimating the burst error positions using syndrome correlation of subcodes which are interleaved m-fold burst error detecting codes, this second method corrects erasure errors in each subcode and m-fold burst errors. The performance of these two methods is analyzed via computer simulation, and their effectiveness is demonstrated.
Toric Varieties and Codes, Error-correcting Codes, Quantum Codes, Secret Sharing and Decoding
DEFF Research Database (Denmark)
Hansen, Johan Peder
We present toric varieties and associated toric codes and their decoding. Toric codes are applied to construct Linear Secret Sharing Schemes (LSSS) with strong multiplication by the Massey construction. Asymmetric Quantum Codes are obtained from toric codes by the A.R. Calderbank P.W. Shor and A.......M. Steane construction of stabilizer codes (CSS) from linear codes containing their dual codes....
A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting
Pan, Xiaofei; Pan, Kegang; Ye, Zhan; Gong, Chao
2014-01-01
We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. PMID:25540813
Remote one-qubit information concentration and decoding of operator quantum error-correction codes
International Nuclear Information System (INIS)
Hsu Liyi
2007-01-01
We propose the general scheme of remote one-qubit information concentration. To achieve the task, the Bell-correlated mixed states are exploited. In addition, the nonremote one-qubit information concentration is equivalent to the decoding of the quantum error-correction code. Here we propose how to decode the stabilizer codes. In particular, the proposed scheme can be used for the operator quantum error-correction codes. The encoded state can be recreated on the errorless qubit, regardless how many bit-flip errors and phase-flip errors have occurred
Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes
Costello, D. J., Jr.; Deng, H.; Lin, S.
1984-01-01
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.
Quantum mean-field decoding algorithm for error-correcting codes
International Nuclear Information System (INIS)
Inoue, Jun-ichi; Saika, Yohei; Okada, Masato
2009-01-01
We numerically examine a quantum version of TAP (Thouless-Anderson-Palmer)-like mean-field algorithm for the problem of error-correcting codes. For a class of the so-called Sourlas error-correcting codes, we check the usefulness to retrieve the original bit-sequence (message) with a finite length. The decoding dynamics is derived explicitly and we evaluate the average-case performance through the bit-error rate (BER).
On the decoding process in ternary error-correcting output codes.
Escalera, Sergio; Pujol, Oriol; Radeva, Petia
2010-01-01
A common way to model multiclass classification problems is to design a set of binary classifiers and to combine them. Error-Correcting Output Codes (ECOC) represent a successful framework to deal with these type of problems. Recent works in the ECOC framework showed significant performance improvements by means of new problem-dependent designs based on the ternary ECOC framework. The ternary framework contains a larger set of binary problems because of the use of a "do not care" symbol that allows us to ignore some classes by a given classifier. However, there are no proper studies that analyze the effect of the new symbol at the decoding step. In this paper, we present a taxonomy that embeds all binary and ternary ECOC decoding strategies into four groups. We show that the zero symbol introduces two kinds of biases that require redefinition of the decoding design. A new type of decoding measure is proposed, and two novel decoding strategies are defined. We evaluate the state-of-the-art coding and decoding strategies over a set of UCI Machine Learning Repository data sets and into a real traffic sign categorization problem. The experimental results show that, following the new decoding strategies, the performance of the ECOC design is significantly improved.
Adaptive decoding of convolutional codes
Directory of Open Access Journals (Sweden)
K. Hueske
2007-06-01
Full Text Available Convolutional codes, which are frequently used as error correction codes in digital transmission systems, are generally decoded using the Viterbi Decoder. On the one hand the Viterbi Decoder is an optimum maximum likelihood decoder, i.e. the most probable transmitted code sequence is obtained. On the other hand the mathematical complexity of the algorithm only depends on the used code, not on the number of transmission errors. To reduce the complexity of the decoding process for good transmission conditions, an alternative syndrome based decoder is presented. The reduction of complexity is realized by two different approaches, the syndrome zero sequence deactivation and the path metric equalization. The two approaches enable an easy adaptation of the decoding complexity for different transmission conditions, which results in a trade-off between decoding complexity and error correction performance.
Adaptive decoding of convolutional codes
Hueske, K.; Geldmacher, J.; Götze, J.
2007-06-01
Convolutional codes, which are frequently used as error correction codes in digital transmission systems, are generally decoded using the Viterbi Decoder. On the one hand the Viterbi Decoder is an optimum maximum likelihood decoder, i.e. the most probable transmitted code sequence is obtained. On the other hand the mathematical complexity of the algorithm only depends on the used code, not on the number of transmission errors. To reduce the complexity of the decoding process for good transmission conditions, an alternative syndrome based decoder is presented. The reduction of complexity is realized by two different approaches, the syndrome zero sequence deactivation and the path metric equalization. The two approaches enable an easy adaptation of the decoding complexity for different transmission conditions, which results in a trade-off between decoding complexity and error correction performance.
Decoding error-correcting codes with Gröbner bases
Bulygin, S.; Pellikaan, G.R.; Veldhuis, R.; Cronie, H.; Hoeksema, H.
2007-01-01
The decoding of arbitrary linear block codes is accomplished by solving a system of quadratic equations by means of Buchberger’s algorithm for finding a Gröbner basis. This generalizes the algorithm of Berlekamp-Massey for decoding Reed Solomon, Goppa and cyclic codes up to half the true minimum
Potts glass reflection of the decoding threshold for qudit quantum error correcting codes
Jiang, Yi; Kovalev, Alexey A.; Pryadko, Leonid P.
We map the maximum likelihood decoding threshold for qudit quantum error correcting codes to the multicritical point in generalized Potts gauge glass models, extending the map constructed previously for qubit codes. An n-qudit quantum LDPC code, where a qudit can be involved in up to m stabilizer generators, corresponds to a ℤd Potts model with n interaction terms which can couple up to m spins each. We analyze general properties of the phase diagram of the constructed model, give several bounds on the location of the transitions, bounds on the energy density of extended defects (non-local analogs of domain walls), and discuss the correlation functions which can be used to distinguish different phases in the original and the dual models. This research was supported in part by the Grants: NSF PHY-1415600 (AAK), NSF PHY-1416578 (LPP), and ARO W911NF-14-1-0272 (LPP).
Bounded distance decoding of linear error-correcting codes with Gröbner bases
Bulygin, S.; Pellikaan, G.R.
2009-01-01
The problem of bounded distance decoding of arbitrary linear codes using Gröbner bases is addressed. A new method is proposed, which is based on reducing an initial decoding problem to solving a certain system of polynomial equations over a finite field. The peculiarity of this system is that, when
Neural Decoder for Topological Codes
Torlai, Giacomo; Melko, Roger G.
2017-07-01
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two-dimensional toric code with phase-flip errors.
Decoding of DBEC-TBED Reed-Solomon codes. [Double-Byte-Error-Correcting, Triple-Byte-Error-Detecting
Deng, Robert H.; Costello, Daniel J., Jr.
1987-01-01
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256 K bit DRAM's are organized in 32 K x 8 bit-bytes. Byte-oriented codes such as Reed-Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. The paper presents a special decoding technique for double-byte-error-correcting, triple-byte-error-detecting RS codes which is capable of high-speed operation. This technique is designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.
Decoding of concatenated codes with interleaved outer codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom; Thommesen, Christian
2004-01-01
Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved (N, K) Reed-Solomon codes, which allows close to N-K errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes.......Recently Bleichenbacher et al. proposed a decoding algorithm for interleaved (N, K) Reed-Solomon codes, which allows close to N-K errors to be corrected in many cases. We discuss the application of this decoding algorithm to concatenated codes....
Decoding linear error-correcting codes up to half the minimum distance with Gröbner bases
Bulygin, S.; Pellikaan, G.R.; Sala, M.; Mora, T.; Perret, L.; Sakata, S.; Traverso, C.
2009-01-01
In this short note we show how one can decode linear error-correcting codes up to half the minimum distance via solving a system of polynomial equations over a finite field. We also explicitly present the reduced Gröbner basis for the system considered.
Indian Academy of Sciences (India)
Shannon limit of the channel. Among the earliest discovered codes that approach the. Shannon limit were the low density parity check (LDPC) codes. The term low density arises from the property of the parity check matrix defining the code. We will now define this matrix and the role that it plays in decoding. 2. Linear Codes.
On Decoding Interleaved Chinese Remainder Codes
DEFF Research Database (Denmark)
Li, Wenhui; Sidorenko, Vladimir; Nielsen, Johan Sebastian Rosenkilde
2013-01-01
We model the decoding of Interleaved Chinese Remainder codes as that of finding a short vector in a Z-lattice. Using the LLL algorithm, we obtain an efficient decoding algorithm, correcting errors beyond the unique decoding bound and having nearly linear complexity. The algorithm can fail...... with a probability dependent on the number of errors, and we give an upper bound for this. Simulation results indicate that the bound is close to the truth. We apply the proposed decoding algorithm for decoding a single CR code using the idea of “Power” decoding, suggested for Reed-Solomon codes. A combination...... of these two methods can be used to decode low-rate Interleaved Chinese Remainder codes....
DEFF Research Database (Denmark)
Nielsen, Rasmus Refslund
2002-01-01
This paper describes an efficient decoding method for a recent construction of good linear codes as well as an extension to the construction. Furthermore, asymptotic properties and list decoding of the codes are discussed.......This paper describes an efficient decoding method for a recent construction of good linear codes as well as an extension to the construction. Furthermore, asymptotic properties and list decoding of the codes are discussed....
Fast decoders for qudit topological codes
International Nuclear Information System (INIS)
Anwar, Hussain; Brown, Benjamin J; Campbell, Earl T; Browne, Dan E
2014-01-01
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However, standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyse their error correction thresholds and efficiency. The first decoder is a generalization of a ‘hard-decisions’ decoder due to Bravyi and Haah (arXiv:1112.3252). We modify this decoder to overcome a percolation effect which limits its threshold performance for many-level quantum systems. The second decoder is a generalization of a ‘soft-decisions’ decoder due to Poulin and Duclos-Cianci (2010 Phys. Rev. Lett. 104 050504), with a small cell size to optimize the efficiency of implementation in the high dimensional case. In each case, we estimate thresholds for the uncorrelated bit-flip error model and provide a comparative analysis of the performance of both these approaches to error correction of qudit toric codes. (paper)
Generalized Sudan's List Decoding for Order Domain Codes
DEFF Research Database (Denmark)
Geil, Hans Olav; Matsumoto, Ryutaroh
2007-01-01
We generalize Sudan's list decoding algorithm without multiplicity to evaluation codes coming from arbitrary order domains. The number of correctable errors by the proposed method is larger than the original list decoding without multiplicity....
Decoding small surface codes with feedforward neural networks
Varsamopoulos, Savvas; Criger, Ben; Bertels, Koen
2018-01-01
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the decoding problem to a classification problem that a feedforward neural network can solve. We investigate quantum error correction and fault tolerance at small code distances using neural network-based decoders, demonstrating that the neural network can generalize to inputs that were not provided during training and that they can reach similar or better decoding performance compared to previous algorithms. We conclude by discussing the time required by a feedforward neural network decoder in hardware.
List Decoding of Algebraic Codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde
We investigate three paradigms for polynomial-time decoding of Reed–Solomon codes beyond half the minimum distance: the Guruswami–Sudan algorithm, Power decoding and the Wu algorithm. The main results concern shaping the computational core of all three methods to a problem solvable by module...... Hermitian codes using Guruswami–Sudan or Power decoding faster than previously known, and we show how to Wu list decode binary Goppa codes....... to solve such using module minimisation, or using our new Demand–Driven algorithm which is also based on module minimisation. The decoding paradigms are all derived and analysed in a self-contained manner, often in new ways or examined in greater depth than previously. Among a number of new results, we...
Indian Academy of Sciences (India)
having a probability Pi of being equal to a 1. Let us assume ... equal to a 0/1 has no bearing on the probability of the. It is often ... bits (call this set S) whose individual bits add up to zero ... In the context of binary error-correct~ng codes, specifi-.
Iterative Decoding of Concatenated Codes: A Tutorial
Directory of Open Access Journals (Sweden)
Phillip A. Regalia
2005-05-01
Full Text Available The turbo decoding algorithm of a decade ago constituted a milestone in error-correction coding for digital communications, and has inspired extensions to generalized receiver topologies, including turbo equalization, turbo synchronization, and turbo CDMA, among others. Despite an accrued understanding of iterative decoding over the years, the Ã¢Â€Âœturbo principleÃ¢Â€Â remains elusive to master analytically, thereby inciting interest from researchers outside the communications domain. In this spirit, we develop a tutorial presentation of iterative decoding for parallel and serial concatenated codes, in terms hopefully accessible to a broader audience. We motivate iterative decoding as a computationally tractable attempt to approach maximum-likelihood decoding, and characterize fixed points in terms of a Ã¢Â€ÂœconsensusÃ¢Â€Â property between constituent decoders. We review how the decoding algorithm for both parallel and serial concatenated codes coincides with an alternating projection algorithm, which allows one to identify conditions under which the algorithm indeed converges to a maximum-likelihood solution, in terms of particular likelihood functions factoring into the product of their marginals. The presentation emphasizes a common framework applicable to both parallel and serial concatenated codes.
Fast decoding algorithms for geometric coded apertures
International Nuclear Information System (INIS)
Byard, Kevin
2015-01-01
Fast decoding algorithms are described for the class of coded aperture designs known as geometric coded apertures which were introduced by Gourlay and Stephen. When compared to the direct decoding method, the algorithms significantly reduce the number of calculations required when performing the decoding for these apertures and hence speed up the decoding process. Experimental tests confirm the efficacy of these fast algorithms, demonstrating a speed up of approximately two to three orders of magnitude over direct decoding.
Toric Codes, Multiplicative Structure and Decoding
DEFF Research Database (Denmark)
Hansen, Johan Peder
2017-01-01
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric codes. The multiplicative structure allows for \\emph{decoding}, resembling the decoding of Reed-Solomon codes and al...
Error-correction coding for digital communications
Clark, G. C., Jr.; Cain, J. B.
This book is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. Fundamental concepts of coding are discussed along with group codes, taking into account basic principles, practical constraints, performance computations, coding bounds, generalized parity check codes, polynomial codes, and important classes of group codes. Other topics explored are related to simple nonalgebraic decoding techniques for group codes, soft decision decoding of block codes, algebraic techniques for multiple error correction, the convolutional code structure and Viterbi decoding, syndrome decoding techniques, and sequential decoding techniques. System applications are also considered, giving attention to concatenated codes, coding for the white Gaussian noise channel, interleaver structures for coded systems, and coding for burst noise channels.
Sudan-decoding generalized geometric Goppa codes
DEFF Research Database (Denmark)
Heydtmann, Agnes Eileen
2003-01-01
Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...... for these codes based on Sudan's improved algorithm is presented and its error-correcting capacity is analyzed. For the implementation of the algorithm it is necessary that the so-called increasing zero bases of certain spaces of functions are available. A method to obtain such bases is developed....
Soft-decision decoding of RS codes
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
By introducing a few simplifying assumptions we derive a simple condition for successful decoding using the Koetter-Vardy algorithm for soft-decision decoding of RS codes. We show that the algorithm has a significant advantage over hard decision decoding when the code rate is low, when two or more...
A class of Sudan-decodable codes
DEFF Research Database (Denmark)
Nielsen, Rasmus Refslund
2000-01-01
In this article, Sudan's algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed-Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based...... on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons with Reed-Solomon and Hermitian codes are made....
Improved decoding for a concatenated coding system
DEFF Research Database (Denmark)
Paaske, Erik
1990-01-01
The concatenated coding system recommended by CCSDS (Consultative Committee for Space Data Systems) uses an outer (255,233) Reed-Solomon (RS) code based on 8-b symbols, followed by the block interleaver and an inner rate 1/2 convolutional code with memory 6. Viterbi decoding is assumed. Two new...... decoding procedures based on repeated decoding trials and exchange of information between the two decoders and the deinterleaver are proposed. In the first one, where the improvement is 0.3-0.4 dB, only the RS decoder performs repeated trials. In the second one, where the improvement is 0.5-0.6 dB, both...... decoders perform repeated decoding trials and decoding information is exchanged between them...
On minimizing the maximum broadcast decoding delay for instantly decodable network coding
Douik, Ahmed S.; Sorour, Sameh; Alouini, Mohamed-Slim; Ai-Naffouri, Tareq Y.
2014-01-01
In this paper, we consider the problem of minimizing the maximum broadcast decoding delay experienced by all the receivers of generalized instantly decodable network coding (IDNC). Unlike the sum decoding delay, the maximum decoding delay as a
Study of bifurcation behavior of two-dimensional turbo product code decoders
International Nuclear Information System (INIS)
He Yejun; Lau, Francis C.M.; Tse, Chi K.
2008-01-01
Turbo codes, low-density parity-check (LDPC) codes and turbo product codes (TPCs) are high performance error-correction codes which employ iterative algorithms for decoding. Under different conditions, the behaviors of the decoders are different. While the nonlinear dynamical behaviors of turbo code decoders and LDPC decoders have been reported in the literature, the dynamical behavior of TPC decoders is relatively unexplored. In this paper, we investigate the behavior of the iterative algorithm of a two-dimensional TPC decoder when the input signal-to-noise ratio (SNR) varies. The quantity to be measured is the mean square value of the posterior probabilities of the information bits. Unlike turbo decoders or LDPC decoders, TPC decoders do not produce a clear 'waterfall region'. This is mainly because the TPC decoding algorithm does not converge to 'indecisive' fixed points even at very low SNR values
Study of bifurcation behavior of two-dimensional turbo product code decoders
Energy Technology Data Exchange (ETDEWEB)
He Yejun [Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hunghom, Hong Kong (China); Lau, Francis C.M. [Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hunghom, Hong Kong (China)], E-mail: encmlau@polyu.edu.hk; Tse, Chi K. [Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hunghom, Hong Kong (China)
2008-04-15
Turbo codes, low-density parity-check (LDPC) codes and turbo product codes (TPCs) are high performance error-correction codes which employ iterative algorithms for decoding. Under different conditions, the behaviors of the decoders are different. While the nonlinear dynamical behaviors of turbo code decoders and LDPC decoders have been reported in the literature, the dynamical behavior of TPC decoders is relatively unexplored. In this paper, we investigate the behavior of the iterative algorithm of a two-dimensional TPC decoder when the input signal-to-noise ratio (SNR) varies. The quantity to be measured is the mean square value of the posterior probabilities of the information bits. Unlike turbo decoders or LDPC decoders, TPC decoders do not produce a clear 'waterfall region'. This is mainly because the TPC decoding algorithm does not converge to 'indecisive' fixed points even at very low SNR values.
Fast decoding of codes from algebraic plane curves
DEFF Research Database (Denmark)
Justesen, Jørn; Larsen, Knud J.; Jensen, Helge Elbrønd
1992-01-01
Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m2 /8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding...
Efficient decoding of random errors for quantum expander codes
Fawzi , Omar; Grospellier , Antoine; Leverrier , Anthony
2017-01-01
We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\\'emor can correct a constant fraction of random errors with very high probability. This is the first construction of a constant-rate quantum LDPC code with an efficient decoding algorithm that can correct a linear number of random errors with a negligible failure probability. Finding codes with these properties is also motivated by Gottes...
Error correcting coding for OTN
DEFF Research Database (Denmark)
Justesen, Jørn; Larsen, Knud J.; Pedersen, Lars A.
2010-01-01
Forward error correction codes for 100 Gb/s optical transmission are currently receiving much attention from transport network operators and technology providers. We discuss the performance of hard decision decoding using product type codes that cover a single OTN frame or a small number...... of such frames. In particular we argue that a three-error correcting BCH is the best choice for the component code in such systems....
An FPGA Implementation of (3,6-Regular Low-Density Parity-Check Code Decoder
Directory of Open Access Journals (Sweden)
Tong Zhang
2003-05-01
Full Text Available Because of their excellent error-correcting performance, low-density parity-check (LDPC codes have recently attracted a lot of attention. In this paper, we are interested in the practical LDPC code decoder hardware implementations. The direct fully parallel decoder implementation usually incurs too high hardware complexity for many real applications, thus partly parallel decoder design approaches that can achieve appropriate trade-offs between hardware complexity and decoding throughput are highly desirable. Applying a joint code and decoder design methodology, we develop a high-speed (3,k-regular LDPC code partly parallel decoder architecture based on which we implement a 9216-bit, rate-1/2(3,6-regular LDPC code decoder on Xilinx FPGA device. This partly parallel decoder supports a maximum symbol throughput of 54 Mbps and achieves BER 10Ã¢ÂˆÂ’6 at 2 dB over AWGN channel while performing maximum 18 decoding iterations.
Decoding Algorithms for Random Linear Network Codes
DEFF Research Database (Denmark)
Heide, Janus; Pedersen, Morten Videbæk; Fitzek, Frank
2011-01-01
We consider the problem of efficient decoding of a random linear code over a finite field. In particular we are interested in the case where the code is random, relatively sparse, and use the binary finite field as an example. The goal is to decode the data using fewer operations to potentially...... achieve a high coding throughput, and reduce energy consumption.We use an on-the-fly version of the Gauss-Jordan algorithm as a baseline, and provide several simple improvements to reduce the number of operations needed to perform decoding. Our tests show that the improvements can reduce the number...
Analysis of Iterated Hard Decision Decoding of Product Codes with Reed-Solomon Component Codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2007-01-01
Products of Reed-Solomon codes are important in applications because they offer a combination of large blocks, low decoding complexity, and good performance. A recent result on random graphs can be used to show that with high probability a large number of errors can be corrected by iterating...... minimum distance decoding. We present an analysis related to density evolution which gives the exact asymptotic value of the decoding threshold and also provides a closed form approximation to the distribution of errors in each step of the decoding of finite length codes....
Concatenated coding system with iterated sequential inner decoding
DEFF Research Database (Denmark)
Jensen, Ole Riis; Paaske, Erik
1995-01-01
We describe a concatenated coding system with iterated sequential inner decoding. The system uses convolutional codes of very long constraint length and operates on iterations between an inner Fano decoder and an outer Reed-Solomon decoder......We describe a concatenated coding system with iterated sequential inner decoding. The system uses convolutional codes of very long constraint length and operates on iterations between an inner Fano decoder and an outer Reed-Solomon decoder...
Multiuser Random Coding Techniques for Mismatched Decoding
Scarlett, Jonathan; Martinez, Alfonso; Guillén i Fàbregas, Albert
2016-01-01
This paper studies multiuser random coding techniques for channel coding with a given (possibly suboptimal) decoding rule. For the mismatched discrete memoryless multiple-access channel, an error exponent is obtained that is tight with respect to the ensemble average, and positive within the interior of Lapidoth's achievable rate region. This exponent proves the ensemble tightness of the exponent of Liu and Hughes in the case of maximum-likelihood decoding. An equivalent dual form of Lapidoth...
Fast decoding algorithms for coded aperture systems
International Nuclear Information System (INIS)
Byard, Kevin
2014-01-01
Fast decoding algorithms are described for a number of established coded aperture systems. The fast decoding algorithms for all these systems offer significant reductions in the number of calculations required when reconstructing images formed by a coded aperture system and hence require less computation time to produce the images. The algorithms may therefore be of use in applications that require fast image reconstruction, such as near real-time nuclear medicine and location of hazardous radioactive spillage. Experimental tests confirm the efficacy of the fast decoding techniques
Multiple LDPC decoding for distributed source coding and video coding
DEFF Research Database (Denmark)
Forchhammer, Søren; Luong, Huynh Van; Huang, Xin
2011-01-01
Distributed source coding (DSC) is a coding paradigm for systems which fully or partly exploit the source statistics at the decoder to reduce the computational burden at the encoder. Distributed video coding (DVC) is one example. This paper considers the use of Low Density Parity Check Accumulate...... (LDPCA) codes in a DSC scheme with feed-back. To improve the LDPC coding performance in the context of DSC and DVC, while retaining short encoder blocks, this paper proposes multiple parallel LDPC decoding. The proposed scheme passes soft information between decoders to enhance performance. Experimental...
Optimal and efficient decoding of concatenated quantum block codes
International Nuclear Information System (INIS)
Poulin, David
2006-01-01
We consider the problem of optimally decoding a quantum error correction code--that is, to find the optimal recovery procedure given the outcomes of partial ''check'' measurements on the system. In general, this problem is NP hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message-passing algorithm. We compare the performance of the message-passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the five-qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message-passing algorithms in two respects: (i) Optimal decoding increases by as much as 94% the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel; and (ii) for noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead
Iterative optimization of quantum error correcting codes
International Nuclear Information System (INIS)
Reimpell, M.; Werner, R.F.
2005-01-01
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds codes outside the usual Knill-Laflamme definition of error correcting codes. The iteration is shown to improve the figure of merit 'channel fidelity' in every step
Low Complexity List Decoding for Polar Codes with Multiple CRC Codes
Directory of Open Access Journals (Sweden)
Jong-Hwan Kim
2017-04-01
Full Text Available Polar codes are the first family of error correcting codes that provably achieve the capacity of symmetric binary-input discrete memoryless channels with low complexity. Since the development of polar codes, there have been many studies to improve their finite-length performance. As a result, polar codes are now adopted as a channel code for the control channel of 5G new radio of the 3rd generation partnership project. However, the decoder implementation is one of the big practical problems and low complexity decoding has been studied. This paper addresses a low complexity successive cancellation list decoding for polar codes utilizing multiple cyclic redundancy check (CRC codes. While some research uses multiple CRC codes to reduce memory and time complexity, we consider the operational complexity of decoding, and reduce it by optimizing CRC positions in combination with a modified decoding operation. Resultingly, the proposed scheme obtains not only complexity reduction from early stopping of decoding, but also additional reduction from the reduced number of decoding paths.
Decoding LDPC Convolutional Codes on Markov Channels
Directory of Open Access Journals (Sweden)
Kashyap Manohar
2008-01-01
Full Text Available Abstract This paper describes a pipelined iterative technique for joint decoding and channel state estimation of LDPC convolutional codes over Markov channels. Example designs are presented for the Gilbert-Elliott discrete channel model. We also compare the performance and complexity of our algorithm against joint decoding and state estimation of conventional LDPC block codes. Complexity analysis reveals that our pipelined algorithm reduces the number of operations per time step compared to LDPC block codes, at the expense of increased memory and latency. This tradeoff is favorable for low-power applications.
Decoding LDPC Convolutional Codes on Markov Channels
Directory of Open Access Journals (Sweden)
Chris Winstead
2008-04-01
Full Text Available This paper describes a pipelined iterative technique for joint decoding and channel state estimation of LDPC convolutional codes over Markov channels. Example designs are presented for the Gilbert-Elliott discrete channel model. We also compare the performance and complexity of our algorithm against joint decoding and state estimation of conventional LDPC block codes. Complexity analysis reveals that our pipelined algorithm reduces the number of operations per time step compared to LDPC block codes, at the expense of increased memory and latency. This tradeoff is favorable for low-power applications.
Codes on the Klein quartic, ideals, and decoding
DEFF Research Database (Denmark)
Hansen, Johan P.
1987-01-01
descriptions as left ideals in the group-algebra GF(2^{3})[G]. This description allows for easy decoding. For instance, in the case of the single error correcting code of length21and dimension16with minimal distance3. decoding is obtained by multiplication with an idempotent in the group algebra.......A sequence of codes with particular symmetries and with large rates compared to their minimal distances is constructed over the field GF(2^{3}). In the sequence there is, for instance, a code of length 21 and dimension10with minimal distance9, and a code of length21and dimension16with minimal...... distance3. The codes are constructed from algebraic geometry using the dictionary between coding theory and algebraic curves over finite fields established by Goppa. The curve used in the present work is the Klein quartic. This curve has the maximal number of rational points over GF(2^{3})allowed by Serre...
Improved Power Decoding of One-Point Hermitian Codes
DEFF Research Database (Denmark)
Puchinger, Sven; Bouw, Irene; Rosenkilde, Johan Sebastian Heesemann
2017-01-01
We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami–Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power...... decoding algorithm for Reed–Solomon codes and does not require an expensive root-finding step. In addition, it promises improvements for decoding interleaved Hermitian codes....
Decoding Hermitian Codes with Sudan's Algorithm
DEFF Research Database (Denmark)
Høholdt, Tom; Nielsen, Rasmus Refslund
1999-01-01
We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q-polynomial, and a reduct......We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q...
Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
DEFF Research Database (Denmark)
Puchinger, Sven; Müelich, Sven; Mödinger, David
2017-01-01
We prove that Alekhnovich's algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ℓ3n(ω+1)/2log(n)) decoding algorithm for ℓ-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent.......We prove that Alekhnovich's algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ℓ3n(ω+1)/2log(n)) decoding algorithm for ℓ-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent....
Linear-time general decoding algorithm for the surface code
Darmawan, Andrew S.; Poulin, David
2018-05-01
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including coherences and correlations. We demonstrate that the decoder significantly outperforms the conventional matching algorithm on a variety of noise models, including non-Pauli noise and spatially correlated noise. The algorithm is based on an approximate calculation of the logical channel using a tensor-network description of the noisy state.
Coding and decoding with dendrites.
Papoutsi, Athanasia; Kastellakis, George; Psarrou, Maria; Anastasakis, Stelios; Poirazi, Panayiota
2014-02-01
Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level. Copyright © 2013 Elsevier Ltd. All rights reserved.
Robust pattern decoding in shape-coded structured light
Tang, Suming; Zhang, Xu; Song, Zhan; Song, Lifang; Zeng, Hai
2017-09-01
Decoding is a challenging and complex problem in a coded structured light system. In this paper, a robust pattern decoding method is proposed for the shape-coded structured light in which the pattern is designed as grid shape with embedded geometrical shapes. In our decoding method, advancements are made at three steps. First, a multi-template feature detection algorithm is introduced to detect the feature point which is the intersection of each two orthogonal grid-lines. Second, pattern element identification is modelled as a supervised classification problem and the deep neural network technique is applied for the accurate classification of pattern elements. Before that, a training dataset is established, which contains a mass of pattern elements with various blurring and distortions. Third, an error correction mechanism based on epipolar constraint, coplanarity constraint and topological constraint is presented to reduce the false matches. In the experiments, several complex objects including human hand are chosen to test the accuracy and robustness of the proposed method. The experimental results show that our decoding method not only has high decoding accuracy, but also owns strong robustness to surface color and complex textures.
Binary Systematic Network Coding for Progressive Packet Decoding
Jones, Andrew L.; Chatzigeorgiou, Ioannis; Tassi, Andrea
2015-01-01
We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show that systematic network coding outperforms conventional net- work coding. We also develop an algorithm based on Gaussian elimination that allows progressive decoding of source packets. Simulation results show that the proposed decoding algorithm can achieve ...
Statistical mechanics of error-correcting codes
Kabashima, Y.; Saad, D.
1999-01-01
We investigate the performance of error-correcting codes, where the code word comprises products of K bits selected from the original message and decoding is carried out utilizing a connectivity tensor with C connections per index. Shannon's bound for the channel capacity is recovered for large K and zero temperature when the code rate K/C is finite. Close to optimal error-correcting capability is obtained for finite K and C. We examine the finite-temperature case to assess the use of simulated annealing for decoding and extend the analysis to accommodate other types of noisy channels.
Bounded-Angle Iterative Decoding of LDPC Codes
Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush
2009-01-01
Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).
Hinds, Erold W. (Principal Investigator)
1996-01-01
This report describes the progress made towards the completion of a specific task on error-correcting coding. The proposed research consisted of investigating the use of modulation block codes as the inner code of a concatenated coding system in order to improve the overall space link communications performance. The study proposed to identify and analyze candidate codes that will complement the performance of the overall coding system which uses the interleaved RS (255,223) code as the outer code.
Fast and Flexible Successive-Cancellation List Decoders for Polar Codes
Hashemi, Seyyed Ali; Condo, Carlo; Gross, Warren J.
2017-11-01
Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL) decoding provides a reasonable trade-off between the error-correction performance and hardware implementation complexity when used to decode polar codes, at the cost of limited throughput. The simplified SCL (SSCL) and its extension SSCL-SPC increase the speed of decoding by removing redundant calculations when encountering particular information and frozen bit patterns (rate one and single parity check codes), while keeping the error-correction performance unaltered. In this paper, we improve SSCL and SSCL-SPC by proving that the list size imposes a specific number of bit estimations required to decode rate one and single parity check codes. Thus, the number of estimations can be limited while guaranteeing exactly the same error-correction performance as if all bits of the code were estimated. We call the new decoding algorithms Fast-SSCL and Fast-SSCL-SPC. Moreover, we show that the number of bit estimations in a practical application can be tuned to achieve desirable speed, while keeping the error-correction performance almost unchanged. Hardware architectures implementing both algorithms are then described and implemented: it is shown that our design can achieve 1.86 Gb/s throughput, higher than the best state-of-the-art decoders.
Probabilistic Amplitude Shaping With Hard Decision Decoding and Staircase Codes
Sheikh, Alireza; Amat, Alexandre Graell i.; Liva, Gianluigi; Steiner, Fabian
2018-05-01
We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by B\\"ocherer \\emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.
Decoding of interleaved Reed-Solomon codes using improved power decoding
DEFF Research Database (Denmark)
Puchinger, Sven; Rosenkilde ne Nielsen, Johan
2017-01-01
We propose a new partial decoding algorithm for m-interleaved Reed-Solomon (IRS) codes that can decode, with high probability, a random error of relative weight 1 − Rm/m+1 at all code rates R, in time polynomial in the code length n. For m > 2, this is an asymptotic improvement over the previous...... state-of-the-art for all rates, and the first improvement for R > 1/3 in the last 20 years. The method combines collaborative decoding of IRS codes with power decoding up to the Johnson radius....
Memory-efficient decoding of LDPC codes
Kwok-San Lee, Jason; Thorpe, Jeremy; Hawkins, Jon
2005-01-01
We present a low-complexity quantization scheme for the implementation of regular (3,6) LDPC codes. The quantization parameters are optimized to maximize the mutual information between the source and the quantized messages. Using this non-uniform quantized belief propagation algorithm, we have simulated that an optimized 3-bit quantizer operates with 0.2dB implementation loss relative to a floating point decoder, and an optimized 4-bit quantizer operates less than 0.1dB quantization loss.
Observations on Polar Coding with CRC-Aided List Decoding
2016-09-01
TECHNICAL REPORT 3041 September 2016 Observations on Polar Coding with CRC-Aided List Decoding David Wasserman Approved for public release. SSC...described in [2, 3]. In FY15 and FY16 we used cyclic redundancy check (CRC)-aided polar list decoding [4]. Section 2 describes the basics of polar coding ...and gives details of the encoders and decoders we used. In the course of our research, we performed simulations of polar codes in hundreds of cases
Polar Coding with CRC-Aided List Decoding
2015-08-01
TECHNICAL REPORT 2087 August 2015 Polar Coding with CRC-Aided List Decoding David Wasserman Approved...list decoding . RESULTS Our simulation results show that polar coding can produce results very similar to the FEC used in the Digital Video...standard. RECOMMENDATIONS In any application for which the DVB-S2 FEC is considered, polar coding with CRC-aided list decod - ing with N = 65536
Iterative channel decoding of FEC-based multiple-description codes.
Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B
2012-03-01
Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.
SYMBOL LEVEL DECODING FOR DUO-BINARY TURBO CODES
Directory of Open Access Journals (Sweden)
Yogesh Beeharry
2017-05-01
Full Text Available This paper investigates the performance of three different symbol level decoding algorithms for Duo-Binary Turbo codes. Explicit details of the computations involved in the three decoding techniques, and a computational complexity analysis are given. Simulation results with different couple lengths, code-rates, and QPSK modulation reveal that the symbol level decoding with bit-level information outperforms the symbol level decoding by 0.1 dB on average in the error floor region. Moreover, a complexity analysis reveals that symbol level decoding with bit-level information reduces the decoding complexity by 19.6 % in terms of the total number of computations required for each half-iteration as compared to symbol level decoding.
Design of a VLSI Decoder for Partially Structured LDPC Codes
Directory of Open Access Journals (Sweden)
Fabrizio Vacca
2008-01-01
of their parity matrix can be partitioned into two disjoint sets, namely, the structured and the random ones. For the proposed class of codes a constructive design method is provided. To assess the value of this method the constructed codes performance are presented. From these results, a novel decoding method called split decoding is introduced. Finally, to prove the effectiveness of the proposed approach a whole VLSI decoder is designed and characterized.
Multi-stage decoding of multi-level modulation codes
Lin, Shu; Kasami, Tadao; Costello, Daniel J., Jr.
1991-01-01
Various types of multi-stage decoding for multi-level modulation codes are investigated. It is shown that if the component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. Particularly, it is shown that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum soft-decision decoding of the code is very small, only a fraction of dB loss in signal to noise ratio at a bit error rate (BER) of 10(exp -6).
Iterative List Decoding of Concatenated Source-Channel Codes
Directory of Open Access Journals (Sweden)
Hedayat Ahmadreza
2005-01-01
Full Text Available Whenever variable-length entropy codes are used in the presence of a noisy channel, any channel errors will propagate and cause significant harm. Despite using channel codes, some residual errors always remain, whose effect will get magnified by error propagation. Mitigating this undesirable effect is of great practical interest. One approach is to use the residual redundancy of variable length codes for joint source-channel decoding. In this paper, we improve the performance of residual redundancy source-channel decoding via an iterative list decoder made possible by a nonbinary outer CRC code. We show that the list decoding of VLC's is beneficial for entropy codes that contain redundancy. Such codes are used in state-of-the-art video coders, for example. The proposed list decoder improves the overall performance significantly in AWGN and fully interleaved Rayleigh fading channels.
Efficient algorithms for maximum likelihood decoding in the surface code
Bravyi, Sergey; Suchara, Martin; Vargo, Alexander
2014-09-01
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the two-dimensional surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time O (n2), where n is the number of code qubits. Our implementation uses a reduction from MLD to simulation of matchgate quantum circuits. This reduction however requires a special noise model with independent bit-flip and phase-flip errors. Secondly, we show how to implement MLD approximately for more general noise models using matrix product states (MPS). Our implementation has running time O (nχ3), where χ is a parameter that controls the approximation precision. The key step of our algorithm, borrowed from the density matrix renormalization-group method, is a subroutine for contracting a tensor network on the two-dimensional grid. The subroutine uses MPS with a bond dimension χ to approximate the sequence of tensors arising in the course of contraction. We benchmark the MPS-based decoder against the standard minimum weight matching decoder observing a significant reduction of the logical error probability for χ ≥4.
Deep Learning Methods for Improved Decoding of Linear Codes
Nachmani, Eliya; Marciano, Elad; Lugosch, Loren; Gross, Warren J.; Burshtein, David; Be'ery, Yair
2018-02-01
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.
On minimizing the maximum broadcast decoding delay for instantly decodable network coding
Douik, Ahmed S.
2014-09-01
In this paper, we consider the problem of minimizing the maximum broadcast decoding delay experienced by all the receivers of generalized instantly decodable network coding (IDNC). Unlike the sum decoding delay, the maximum decoding delay as a definition of delay for IDNC allows a more equitable distribution of the delays between the different receivers and thus a better Quality of Service (QoS). In order to solve this problem, we first derive the expressions for the probability distributions of maximum decoding delay increments. Given these expressions, we formulate the problem as a maximum weight clique problem in the IDNC graph. Although this problem is known to be NP-hard, we design a greedy algorithm to perform effective packet selection. Through extensive simulations, we compare the sum decoding delay and the max decoding delay experienced when applying the policies to minimize the sum decoding delay and our policy to reduce the max decoding delay. Simulations results show that our policy gives a good agreement among all the delay aspects in all situations and outperforms the sum decoding delay policy to effectively minimize the sum decoding delay when the channel conditions become harsher. They also show that our definition of delay significantly improve the number of served receivers when they are subject to strict delay constraints.
On decoding of multi-level MPSK modulation codes
Lin, Shu; Gupta, Alok Kumar
1990-01-01
The decoding problem of multi-level block modulation codes is investigated. The hardware design of soft-decision Viterbi decoder for some short length 8-PSK block modulation codes is presented. An effective way to reduce the hardware complexity of the decoder by reducing the branch metric and path metric, using a non-uniform floating-point to integer mapping scheme, is proposed and discussed. The simulation results of the design are presented. The multi-stage decoding (MSD) of multi-level modulation codes is also investigated. The cases of soft-decision and hard-decision MSD are considered and their performance are evaluated for several codes of different lengths and different minimum squared Euclidean distances. It is shown that the soft-decision MSD reduces the decoding complexity drastically and it is suboptimum. The hard-decision MSD further simplifies the decoding while still maintaining a reasonable coding gain over the uncoded system, if the component codes are chosen properly. Finally, some basic 3-level 8-PSK modulation codes using BCH codes as component codes are constructed and their coding gains are found for hard decision multistage decoding.
On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes
DEFF Research Database (Denmark)
Beelen, Peter; Høholdt, Tom; Nielsen, Johan Sebastian Rosenkilde
2013-01-01
We derive the Wu list-decoding algorithm for generalized Reed–Solomon (GRS) codes by using Gröbner bases over modules and the Euclidean algorithm as the initial algorithm instead of the Berlekamp–Massey algorithm. We present a novel method for constructing the interpolation polynomial fast. We gi...... and a duality in the choice of parameters needed for decoding, both in the case of GRS codes and in the case of Goppa codes....
Statistical coding and decoding of heartbeat intervals.
Lucena, Fausto; Barros, Allan Kardec; Príncipe, José C; Ohnishi, Noboru
2011-01-01
The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.
Statistical coding and decoding of heartbeat intervals.
Directory of Open Access Journals (Sweden)
Fausto Lucena
Full Text Available The heart integrates neuroregulatory messages into specific bands of frequency, such that the overall amplitude spectrum of the cardiac output reflects the variations of the autonomic nervous system. This modulatory mechanism seems to be well adjusted to the unpredictability of the cardiac demand, maintaining a proper cardiac regulation. A longstanding theory holds that biological organisms facing an ever-changing environment are likely to evolve adaptive mechanisms to extract essential features in order to adjust their behavior. The key question, however, has been to understand how the neural circuitry self-organizes these feature detectors to select behaviorally relevant information. Previous studies in computational perception suggest that a neural population enhances information that is important for survival by minimizing the statistical redundancy of the stimuli. Herein we investigate whether the cardiac system makes use of a redundancy reduction strategy to regulate the cardiac rhythm. Based on a network of neural filters optimized to code heartbeat intervals, we learn a population code that maximizes the information across the neural ensemble. The emerging population code displays filter tuning proprieties whose characteristics explain diverse aspects of the autonomic cardiac regulation, such as the compromise between fast and slow cardiac responses. We show that the filters yield responses that are quantitatively similar to observed heart rate responses during direct sympathetic or parasympathetic nerve stimulation. Our findings suggest that the heart decodes autonomic stimuli according to information theory principles analogous to how perceptual cues are encoded by sensory systems.
Coding and decoding for code division multiple user communication systems
Healy, T. J.
1985-01-01
A new algorithm is introduced which decodes code division multiple user communication signals. The algorithm makes use of the distinctive form or pattern of each signal to separate it from the composite signal created by the multiple users. Although the algorithm is presented in terms of frequency-hopped signals, the actual transmitter modulator can use any of the existing digital modulation techniques. The algorithm is applicable to error-free codes or to codes where controlled interference is permitted. It can be used when block synchronization is assumed, and in some cases when it is not. The paper also discusses briefly some of the codes which can be used in connection with the algorithm, and relates the algorithm to past studies which use other approaches to the same problem.
A quantum algorithm for Viterbi decoding of classical convolutional codes
Grice, Jon R.; Meyer, David A.
2014-01-01
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper the proposed algorithm is applied to decoding classical convolutional codes, for instance; large constraint length $Q$ and short decode frames $N$. Other applications of the classical Viterbi algorithm where $Q$ is large (e.g. speech processing) could experience significant speedup with the QVA. The QVA exploits the fact that the decoding trellis is similar to the butter...
Probability of undetected error after decoding for a concatenated coding scheme
Costello, D. J., Jr.; Lin, S.
1984-01-01
A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.
Construction and decoding of matrix-product codes from nested codes
DEFF Research Database (Denmark)
Hernando, Fernando; Lally, Kristine; Ruano, Diego
2009-01-01
We consider matrix-product codes [C1 ... Cs] · A, where C1, ..., Cs are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance....
Indian Academy of Sciences (India)
Science and Automation at ... the Reed-Solomon code contained 223 bytes of data, (a byte ... then you have a data storage system with error correction, that ..... practical codes, storing such a table is infeasible, as it is generally too large.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 3. Error Correcting Codes - Reed Solomon Codes. Priti Shankar. Series Article Volume 2 Issue 3 March ... Author Affiliations. Priti Shankar1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India ...
LDPC Codes--Structural Analysis and Decoding Techniques
Zhang, Xiaojie
2012-01-01
Low-density parity-check (LDPC) codes have been the focus of much research over the past decade thanks to their near Shannon limit performance and to their efficient message-passing (MP) decoding algorithms. However, the error floor phenomenon observed in MP decoding, which manifests itself as an abrupt change in the slope of the error-rate curve,…
Locally decodable codes and private information retrieval schemes
Yekhanin, Sergey
2010-01-01
Locally decodable codes (LDCs) are codes that simultaneously provide efficient random access retrieval and high noise resilience by allowing reliable reconstruction of an arbitrary bit of a message by looking at only a small number of randomly chosen codeword bits. Local decodability comes with a certain loss in terms of efficiency - specifically, locally decodable codes require longer codeword lengths than their classical counterparts. Private information retrieval (PIR) schemes are cryptographic protocols designed to safeguard the privacy of database users. They allow clients to retrieve rec
Sub-quadratic decoding of one-point hermitian codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Beelen, Peter
2015-01-01
We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power...... decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities....
Unitary Application of the Quantum Error Correction Codes
International Nuclear Information System (INIS)
You Bo; Xu Ke; Wu Xiaohua
2012-01-01
For applying the perfect code to transmit quantum information over a noise channel, the standard protocol contains four steps: the encoding, the noise channel, the error-correction operation, and the decoding. In present work, we show that this protocol can be simplified. The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation. We also offer a quantum circuit, which can correct the arbitrary single-qubit errors.
Video coding for decoding power-constrained embedded devices
Lu, Ligang; Sheinin, Vadim
2004-01-01
Low power dissipation and fast processing time are crucial requirements for embedded multimedia devices. This paper presents a technique in video coding to decrease the power consumption at a standard video decoder. Coupled with a small dedicated video internal memory cache on a decoder, the technique can substantially decrease the amount of data traffic to the external memory at the decoder. A decrease in data traffic to the external memory at decoder will result in multiple benefits: faster real-time processing and power savings. The encoder, given prior knowledge of the decoder"s dedicated video internal memory cache management scheme, regulates its choice of motion compensated predictors to reduce the decoder"s external memory accesses. This technique can be used in any standard or proprietary encoder scheme to generate a compliant output bit stream decodable by standard CPU-based and dedicated hardware-based decoders for power savings with the best quality-power cost trade off. Our simulation results show that with a relatively small amount of dedicated video internal memory cache, the technique may decrease the traffic between CPU and external memory over 50%.
Rate Aware Instantly Decodable Network Codes
Douik, Ahmed
2016-02-26
This paper addresses the problem of reducing the delivery time of data messages to cellular users using instantly decodable network coding (IDNC) with physical-layer rate awareness. While most of the existing literature on IDNC does not consider any physical layer complications, this paper proposes a cross-layer scheme that incorporates the different channel rates of the various users in the decision process of both the transmitted message combinations and the rates with which they are transmitted. The completion time minimization problem in such scenario is first shown to be intractable. The problem is, thus, approximated by reducing, at each transmission, the increase of an anticipated version of the completion time. The paper solves the problem by formulating it as a maximum weight clique problem over a newly designed rate aware IDNC (RA-IDNC) graph. Further, the paper provides a multi-layer solution to improve the completion time approximation. Simulation results suggest that the cross-layer design largely outperforms the uncoded transmissions strategies and the classical IDNC scheme. © 2015 IEEE.
Rate Aware Instantly Decodable Network Codes
Douik, Ahmed; Sorour, Sameh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
This paper addresses the problem of reducing the delivery time of data messages to cellular users using instantly decodable network coding (IDNC) with physical-layer rate awareness. While most of the existing literature on IDNC does not consider any physical layer complications, this paper proposes a cross-layer scheme that incorporates the different channel rates of the various users in the decision process of both the transmitted message combinations and the rates with which they are transmitted. The completion time minimization problem in such scenario is first shown to be intractable. The problem is, thus, approximated by reducing, at each transmission, the increase of an anticipated version of the completion time. The paper solves the problem by formulating it as a maximum weight clique problem over a newly designed rate aware IDNC (RA-IDNC) graph. Further, the paper provides a multi-layer solution to improve the completion time approximation. Simulation results suggest that the cross-layer design largely outperforms the uncoded transmissions strategies and the classical IDNC scheme. © 2015 IEEE.
Decoding Reed-Solomon Codes beyond half the minimum distance
DEFF Research Database (Denmark)
Høholdt, Tom; Nielsen, Rasmus Refslund
1999-01-01
We describe an efficient implementation of M.Sudan"s algorithm for decoding Reed-Solomon codes beyond half the minimum distance. Furthermore we calculate an upper bound of the probabilty of getting more than one codeword as output...
Performance Analysis of a Decoding Algorithm for Algebraic Geometry Codes
DEFF Research Database (Denmark)
Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund; Høholdt, Tom
1998-01-01
We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is greater than or equal to [(dFR-1)/2]+1, where dFR is the Feng-Rao distance......We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is greater than or equal to [(dFR-1)/2]+1, where dFR is the Feng-Rao distance...
Recent results in the decoding of Algebraic geometry codes
DEFF Research Database (Denmark)
Høholdt, Tom; Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund
1998-01-01
We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is [(dFR-1)/2]+1, where dFR is the Feng-Rao distance......We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is [(dFR-1)/2]+1, where dFR is the Feng-Rao distance...
Directory of Open Access Journals (Sweden)
Johann A. Briffa
2014-06-01
Full Text Available In this study, the authors consider time-varying block (TVB codes, which generalise a number of previous synchronisation error-correcting codes. They also consider various practical issues related to maximum a posteriori (MAP decoding of these codes. Specifically, they give an expression for the expected distribution of drift between transmitter and receiver because of synchronisation errors. They determine an appropriate choice for state space limits based on the drift probability distribution. In turn, they obtain an expression for the decoder complexity under given channel conditions in terms of the state space limits used. For a given state space, they also give a number of optimisations that reduce the algorithm complexity with no further loss of decoder performance. They also show how the MAP decoder can be used in the absence of known frame boundaries, and demonstrate that an appropriate choice of decoder parameters allows the decoder to approach the performance when frame boundaries are known, at the expense of some increase in complexity. Finally, they express some existing constructions as TVB codes, comparing performance with published results and showing that improved performance is possible by taking advantage of the flexibility of TVB codes.
Error Correcting Codes -34 ...
Indian Academy of Sciences (India)
information and coding theory. A large scale relay computer had failed to deliver the expected results due to a hardware fault. Hamming, one of the active proponents of computer usage, was determined to find an efficient means by which computers could detect and correct their own faults. A mathematician by train-.
Construction and decoding of a class of algebraic geometry codes
DEFF Research Database (Denmark)
Justesen, Jørn; Larsen, Knud J.; Jensen, Helge Elbrønd
1989-01-01
A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decod...... is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes......A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result...
"ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"
Energy Technology Data Exchange (ETDEWEB)
SANTHI, NANDAKISHORE [Los Alamos National Laboratory
2007-01-22
We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relative error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.
Iterative demodulation and decoding of coded non-square QAM
Li, L.; Divsalar, D.; Dolinar, S.
2003-01-01
Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM performs 0.5 dB better than standard 8QAM and 0.7 dB better than 8PSK at BER= 10(sup -5), when the FEC code is the (15, 11) Hamming code concatenated with a rate-1 accumulator code, while coded NS-32QAM performs 0.25 dB better than standard 32QAM.
O2-GIDNC: Beyond instantly decodable network coding
Aboutorab, Neda
2013-06-01
In this paper, we are concerned with extending the graph representation of generalized instantly decodable network coding (GIDNC) to a more general opportunistic network coding (ONC) scenario, referred to as order-2 GIDNC (O2-GIDNC). In the O2-GIDNC scheme, receivers can store non-instantly decodable packets (NIDPs) comprising two of their missing packets, and use them in a systematic way for later decodings. Once this graph representation is found, it can be used to extend the GIDNC graph-based analyses to the proposed O2-GIDNC scheme with a limited increase in complexity. In the proposed O2-GIDNC scheme, the information of the stored NIDPs at the receivers and the decoding opportunities they create can be exploited to improve the broadcast completion time and decoding delay compared to traditional GIDNC scheme. The completion time and decoding delay minimizing algorithms that can operate on the new O2-GIDNC graph are further described. The simulation results show that our proposed O2-GIDNC improves the completion time and decoding delay performance of the traditional GIDNC. © 2013 IEEE.
Implementation of Layered Decoding Architecture for LDPC Code using Layered Min-Sum Algorithm
Sandeep Kakde; Atish Khobragade; Shrikant Ambatkar; Pranay Nandanwar
2017-01-01
For binary field and long code lengths, Low Density Parity Check (LDPC) code approaches Shannon limit performance. LDPC codes provide remarkable error correction performance and therefore enlarge the design space for communication systems.In this paper, we have compare different digital modulation techniques and found that BPSK modulation technique is better than other modulation techniques in terms of BER. It also gives error performance of LDPC decoder over AWGN channel using Min-Sum algori...
Completion time reduction in instantly decodable network coding through decoding delay control
Douik, Ahmed S.
2014-12-01
For several years, the completion time and the decoding delay problems in Instantly Decodable Network Coding (IDNC) were considered separately and were thought to completely act against each other. Recently, some works aimed to balance the effects of these two important IDNC metrics but none of them studied a further optimization of one by controlling the other. In this paper, we study the effect of controlling the decoding delay to reduce the completion time below its currently best known solution. We first derive the decoding-delay-dependent expressions of the users\\' and their overall completion times. Although using such expressions to find the optimal overall completion time is NP-hard, we use a heuristic that minimizes the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Simulation results show that this new algorithm achieves both a lower mean completion time and mean decoding delay compared to the best known heuristic for completion time reduction. The gap in performance becomes significant for harsh erasure scenarios.
Completion time reduction in instantly decodable network coding through decoding delay control
Douik, Ahmed S.; Sorour, Sameh; Alouini, Mohamed-Slim; Al-Naffouri, Tareq Y.
2014-01-01
For several years, the completion time and the decoding delay problems in Instantly Decodable Network Coding (IDNC) were considered separately and were thought to completely act against each other. Recently, some works aimed to balance the effects of these two important IDNC metrics but none of them studied a further optimization of one by controlling the other. In this paper, we study the effect of controlling the decoding delay to reduce the completion time below its currently best known solution. We first derive the decoding-delay-dependent expressions of the users' and their overall completion times. Although using such expressions to find the optimal overall completion time is NP-hard, we use a heuristic that minimizes the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Simulation results show that this new algorithm achieves both a lower mean completion time and mean decoding delay compared to the best known heuristic for completion time reduction. The gap in performance becomes significant for harsh erasure scenarios.
Power decoding Reed-Solomon codes up to the Johnson radius
DEFF Research Database (Denmark)
Rosenkilde, Johan Sebastian Heesemann
2018-01-01
Power decoding, or "decoding using virtual interleaving" is a technique for decoding Reed-Solomon codes up to the Sudan radius. Since the method's inception, it has been an open question if it is possible to use this approach to decode up to the Johnson radius - the decoding radius of the Guruswami...
Performance analysis of a decoding algorithm for algebraic-geometry codes
DEFF Research Database (Denmark)
Høholdt, Tom; Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund
1999-01-01
The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out...
Techniques and Architectures for Hazard-Free Semi-Parallel Decoding of LDPC Codes
Directory of Open Access Journals (Sweden)
Rovini Massimo
2009-01-01
Full Text Available The layered decoding algorithm has recently been proposed as an efficient means for the decoding of low-density parity-check (LDPC codes, thanks to the remarkable improvement in the convergence speed (2x of the decoding process. However, pipelined semi-parallel decoders suffer from violations or "hazards" between consecutive updates, which not only violate the layered principle but also enforce the loops in the code, thus spoiling the error correction performance. This paper describes three different techniques to properly reschedule the decoding updates, based on the careful insertion of "idle" cycles, to prevent the hazards of the pipeline mechanism. Also, different semi-parallel architectures of a layered LDPC decoder suitable for use with such techniques are analyzed. Then, taking the LDPC codes for the wireless local area network (IEEE 802.11n as a case study, a detailed analysis of the performance attained with the proposed techniques and architectures is reported, and results of the logic synthesis on a 65 nm low-power CMOS technology are shown.
The fast decoding of Reed-Solomon codes using high-radix fermat theoretic transforms
Liu, K. Y.; Reed, I. S.; Truong, T. K.
1976-01-01
Fourier-like transforms over GF(F sub n), where F sub n = 2(2n) + 1 is a Fermat prime, are applied in decoding Reed-Solomon codes. It is shown that such transforms can be computed using high-radix fast Fourier transform (FFT) algorithms requiring considerably fewer multiplications than the more usual radix 2 FFT algorithm. A special 256-symbol, 16-symbol-error-correcting, Reed-Solomon (RS) code for space communication-link applications can be encoded and decoded using this high-radix FFT algorithm over GF(F sub 3).
O2-GIDNC: Beyond instantly decodable network coding
Aboutorab, Neda; Sorour, Sameh; Sadeghi, Parastoo
2013-01-01
In this paper, we are concerned with extending the graph representation of generalized instantly decodable network coding (GIDNC) to a more general opportunistic network coding (ONC) scenario, referred to as order-2 GIDNC (O2-GIDNC). In the O2-GIDNC
High-speed architecture for the decoding of trellis-coded modulation
Osborne, William P.
1992-01-01
Since 1971, when the Viterbi Algorithm was introduced as the optimal method of decoding convolutional codes, improvements in circuit technology, especially VLSI, have steadily increased its speed and practicality. Trellis-Coded Modulation (TCM) combines convolutional coding with higher level modulation (non-binary source alphabet) to provide forward error correction and spectral efficiency. For binary codes, the current stare-of-the-art is a 64-state Viterbi decoder on a single CMOS chip, operating at a data rate of 25 Mbps. Recently, there has been an interest in increasing the speed of the Viterbi Algorithm by improving the decoder architecture, or by reducing the algorithm itself. Designs employing new architectural techniques are now in existence, however these techniques are currently applied to simpler binary codes, not to TCM. The purpose of this report is to discuss TCM architectural considerations in general, and to present the design, at the logic gate level, or a specific TCM decoder which applies these considerations to achieve high-speed decoding.
Lin, Shu; Fossorier, Marc
1998-01-01
In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm.
Joint Estimation and Decoding of Space-Time Trellis Codes
Directory of Open Access Journals (Sweden)
Zhang Jianqiu
2002-01-01
Full Text Available We explore the possibility of using an emerging tool in statistical signal processing, sequential importance sampling (SIS, for joint estimation and decoding of space-time trellis codes (STTC. First, we provide background on SIS, and then we discuss its application to space-time trellis code (STTC systems. It is shown through simulations that SIS is suitable for joint estimation and decoding of STTC with time-varying flat-fading channels when phase ambiguity is avoided. We used a design criterion for STTCs and temporally correlated channels that combats phase ambiguity without pilot signaling. We have shown by simulations that the design is valid.
Min-Max decoding for non binary LDPC codes
Savin, Valentin
2008-01-01
Iterative decoding of non-binary LDPC codes is currently performed using either the Sum-Product or the Min-Sum algorithms or slightly different versions of them. In this paper, several low-complexity quasi-optimal iterative algorithms are proposed for decoding non-binary codes. The Min-Max algorithm is one of them and it has the benefit of two possible LLR domain implementations: a standard implementation, whose complexity scales as the square of the Galois field's cardinality and a reduced c...
Distributed coding/decoding complexity in video sensor networks.
Cordeiro, Paulo J; Assunção, Pedro
2012-01-01
Video Sensor Networks (VSNs) are recent communication infrastructures used to capture and transmit dense visual information from an application context. In such large scale environments which include video coding, transmission and display/storage, there are several open problems to overcome in practical implementations. This paper addresses the most relevant challenges posed by VSNs, namely stringent bandwidth usage and processing time/power constraints. In particular, the paper proposes a novel VSN architecture where large sets of visual sensors with embedded processors are used for compression and transmission of coded streams to gateways, which in turn transrate the incoming streams and adapt them to the variable complexity requirements of both the sensor encoders and end-user decoder terminals. Such gateways provide real-time transcoding functionalities for bandwidth adaptation and coding/decoding complexity distribution by transferring the most complex video encoding/decoding tasks to the transcoding gateway at the expense of a limited increase in bit rate. Then, a method to reduce the decoding complexity, suitable for system-on-chip implementation, is proposed to operate at the transcoding gateway whenever decoders with constrained resources are targeted. The results show that the proposed method achieves good performance and its inclusion into the VSN infrastructure provides an additional level of complexity control functionality.
List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
DEFF Research Database (Denmark)
Hernando, Fernando; Høholdt, Tom; Ruano, Diego
2012-01-01
A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list...... decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units....
Real-time minimal-bit-error probability decoding of convolutional codes
Lee, L.-N.
1974-01-01
A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.
Real-time minimal bit error probability decoding of convolutional codes
Lee, L. N.
1973-01-01
A recursive procedure is derived for decoding of rate R=1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e. fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications such as in the inner coding system for concatenated coding.
Partially blind instantly decodable network codes for lossy feedback environment
Sorour, Sameh
2014-09-01
In this paper, we study the multicast completion and decoding delay minimization problems for instantly decodable network coding (IDNC) in the case of lossy feedback. When feedback loss events occur, the sender falls into uncertainties about packet reception at the different receivers, which forces it to perform partially blind selections of packet combinations in subsequent transmissions. To determine efficient selection policies that reduce the completion and decoding delays of IDNC in such an environment, we first extend the perfect feedback formulation in our previous works to the lossy feedback environment, by incorporating the uncertainties resulting from unheard feedback events in these formulations. For the completion delay problem, we use this formulation to identify the maximum likelihood state of the network in events of unheard feedback and employ it to design a partially blind graph update extension to the multicast IDNC algorithm in our earlier work. For the decoding delay problem, we derive an expression for the expected decoding delay increment for any arbitrary transmission. This expression is then used to find the optimal policy that reduces the decoding delay in such lossy feedback environment. Results show that our proposed solutions both outperform previously proposed approaches and achieve tolerable degradation even at relatively high feedback loss rates.
Massey, J. L.
1976-01-01
The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.
Soft decoding a self-dual (48, 24; 12) code
Solomon, G.
1993-01-01
A self-dual (48,24;12) code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix, adding an eighth all-zero column, and then adjoining six dimensions to this extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. A soft decoding using these properties and approximating maximum likelihood is presented here. This is preliminary to a possible soft decoding of the box (72,36;15) code that promises a 7.7-dB theoretical coding under maximum likelihood.
Performance Analysis of CRC Codes for Systematic and Nonsystematic Polar Codes with List Decoding
Directory of Open Access Journals (Sweden)
Takumi Murata
2018-01-01
Full Text Available Successive cancellation list (SCL decoding of polar codes is an effective approach that can significantly outperform the original successive cancellation (SC decoding, provided that proper cyclic redundancy-check (CRC codes are employed at the stage of candidate selection. Previous studies on CRC-assisted polar codes mostly focus on improvement of the decoding algorithms as well as their implementation, and little attention has been paid to the CRC code structure itself. For the CRC-concatenated polar codes with CRC code as their outer code, the use of longer CRC code leads to reduction of information rate, whereas the use of shorter CRC code may reduce the error detection probability, thus degrading the frame error rate (FER performance. Therefore, CRC codes of proper length should be employed in order to optimize the FER performance for a given signal-to-noise ratio (SNR per information bit. In this paper, we investigate the effect of CRC codes on the FER performance of polar codes with list decoding in terms of the CRC code length as well as its generator polynomials. Both the original nonsystematic and systematic polar codes are considered, and we also demonstrate that different behaviors of CRC codes should be observed depending on whether the inner polar code is systematic or not.
Decoding Delay Controlled Completion Time Reduction in Instantly Decodable Network Coding
Douik, Ahmed
2016-06-27
For several years, the completion time and the decoding delay problems in Instantly Decodable Network Coding (IDNC) were considered separately and were thought to act completely against each other. Recently, some works aimed to balance the effects of these two important IDNC metrics but none of them studied a further optimization of one by controlling the other. This paper investigates the effect of controlling the decoding delay to reduce the completion time below its currently best-known solution in both perfect and imperfect feedback with persistent erasure channels. To solve the problem, the decodingdelay- dependent expressions of the users’ and overall completion times are derived in the complete feedback scenario. Although using such expressions to find the optimal overall completion time is NP-hard, the paper proposes two novel heuristics that minimizes the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Afterward, the paper extends the study to the imperfect feedback scenario in which uncertainties at the sender affects its ability to anticipate accurately the decoding delay increase at each user. The paper formulates the problem in such environment and derives the expression of the minimum increase in the completion time. Simulation results show the performance of the proposed solutions and suggest that both heuristics achieves a lower mean completion time as compared to the best-known heuristics for the completion time reduction in perfect and imperfect feedback. The gap in performance becomes more significant as the erasure of the channel increases.
Decoding Delay Controlled Completion Time Reduction in Instantly Decodable Network Coding
Douik, Ahmed S.; Sorour, Sameh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2016-01-01
For several years, the completion time and the decoding delay problems in Instantly Decodable Network Coding (IDNC) were considered separately and were thought to act completely against each other. Recently, some works aimed to balance the effects of these two important IDNC metrics but none of them studied a further optimization of one by controlling the other. This paper investigates the effect of controlling the decoding delay to reduce the completion time below its currently best-known solution in both perfect and imperfect feedback with persistent erasure channels. To solve the problem, the decodingdelay- dependent expressions of the users’ and overall completion times are derived in the complete feedback scenario. Although using such expressions to find the optimal overall completion time is NP-hard, the paper proposes two novel heuristics that minimizes the probability of increasing the maximum of these decoding-delay-dependent completion time expressions after each transmission through a layered control of their decoding delays. Afterward, the paper extends the study to the imperfect feedback scenario in which uncertainties at the sender affects its ability to anticipate accurately the decoding delay increase at each user. The paper formulates the problem in such environment and derives the expression of the minimum increase in the completion time. Simulation results show the performance of the proposed solutions and suggest that both heuristics achieves a lower mean completion time as compared to the best-known heuristics for the completion time reduction in perfect and imperfect feedback. The gap in performance becomes more significant as the erasure of the channel increases.
Peeling Decoding of LDPC Codes with Applications in Compressed Sensing
Directory of Open Access Journals (Sweden)
Weijun Zeng
2016-01-01
Full Text Available We present a new approach for the analysis of iterative peeling decoding recovery algorithms in the context of Low-Density Parity-Check (LDPC codes and compressed sensing. The iterative recovery algorithm is particularly interesting for its low measurement cost and low computational complexity. The asymptotic analysis can track the evolution of the fraction of unrecovered signal elements in each iteration, which is similar to the well-known density evolution analysis in the context of LDPC decoding algorithm. Our analysis shows that there exists a threshold on the density factor; if under this threshold, the recovery algorithm is successful; otherwise it will fail. Simulation results are also provided for verifying the agreement between the proposed asymptotic analysis and recovery algorithm. Compared with existing works of peeling decoding algorithm, focusing on the failure probability of the recovery algorithm, our proposed approach gives accurate evolution of performance with different parameters of measurement matrices and is easy to implement. We also show that the peeling decoding algorithm performs better than other schemes based on LDPC codes.
The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions
Reed, I. S.; Scholtz, R. A.; Welch, L. R.; Truong, T. K.
1978-01-01
It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.
Multiple-Symbol Noncoherent Decoding of Uncoded and Convolutionally Codes Continous Phase Modulation
Divsalar, D.; Raphaeli, D.
2000-01-01
Recently, a method for combined noncoherent detection and decoding of trellis-codes (noncoherent coded modulation) has been proposed, which can practically approach the performance of coherent detection.
Central Decoding for Multiple Description Codes based on Domain Partitioning
Directory of Open Access Journals (Sweden)
M. Spiertz
2006-01-01
Full Text Available Multiple Description Codes (MDC can be used to trade redundancy against packet loss resistance for transmitting data over lossy diversity networks. In this work we focus on MD transform coding based on domain partitioning. Compared to Vaishampayan’s quantizer based MDC, domain based MD coding is a simple approach for generating different descriptions, by using different quantizers for each description. Commonly, only the highest rate quantizer is used for reconstruction. In this paper we investigate the benefit of using the lower rate quantizers to enhance the reconstruction quality at decoder side. The comparison is done on artificial source data and on image data.
Improved Iterative Decoding of Network-Channel Codes for Multiple-Access Relay Channel.
Majumder, Saikat; Verma, Shrish
2015-01-01
Cooperative communication using relay nodes is one of the most effective means of exploiting space diversity for low cost nodes in wireless network. In cooperative communication, users, besides communicating their own information, also relay the information of other users. In this paper we investigate a scheme where cooperation is achieved using a common relay node which performs network coding to provide space diversity for two information nodes transmitting to a base station. We propose a scheme which uses Reed-Solomon error correcting code for encoding the information bit at the user nodes and convolutional code as network code, instead of XOR based network coding. Based on this encoder, we propose iterative soft decoding of joint network-channel code by treating it as a concatenated Reed-Solomon convolutional code. Simulation results show significant improvement in performance compared to existing scheme based on compound codes.
Fast decoder for local quantum codes using Groebner basis
Haah, Jeongwan
2013-03-01
Based on arXiv:1204.1063. A local translation-invariant quantum code has a description in terms of Laurent polynomials. As an application of this observation, we present a fast decoding algorithm for translation-invariant local quantum codes in any spatial dimensions using the straightforward division algorithm for multivariate polynomials. The running time is O (n log n) on average, or O (n2 log n) on worst cases, where n is the number of physical qubits. The algorithm improves a subroutine of the renormalization-group decoder by Bravyi and Haah (arXiv:1112.3252) in the translation-invariant case. This work is supported in part by the Insitute for Quantum Information and Matter, an NSF Physics Frontier Center, and the Korea Foundation for Advanced Studies.
Multi-stage decoding for multi-level block modulation codes
Lin, Shu
1991-01-01
In this paper, we investigate various types of multi-stage decoding for multi-level block modulation codes, in which the decoding of a component code at each stage can be either soft-decision or hard-decision, maximum likelihood or bounded-distance. Error performance of codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. Based on our study and computation results, we find that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. In particular, we find that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum decoding of the overall code is very small: only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.
A quantum algorithm for Viterbi decoding of classical convolutional codes
Grice, Jon R.; Meyer, David A.
2015-07-01
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper, the proposed algorithm is applied to decoding classical convolutional codes, for instance, large constraint length and short decode frames . Other applications of the classical Viterbi algorithm where is large (e.g., speech processing) could experience significant speedup with the QVA. The QVA exploits the fact that the decoding trellis is similar to the butterfly diagram of the fast Fourier transform, with its corresponding fast quantum algorithm. The tensor-product structure of the butterfly diagram corresponds to a quantum superposition that we show can be efficiently prepared. The quantum speedup is possible because the performance of the QVA depends on the fanout (number of possible transitions from any given state in the hidden Markov model) which is in general much less than . The QVA constructs a superposition of states which correspond to all legal paths through the decoding lattice, with phase as a function of the probability of the path being taken given received data. A specialized amplitude amplification procedure is applied one or more times to recover a superposition where the most probable path has a high probability of being measured.
Architecture for time or transform domain decoding of reed-solomon codes
Shao, Howard M. (Inventor); Truong, Trieu-Kie (Inventor); Hsu, In-Shek (Inventor); Deutsch, Leslie J. (Inventor)
1989-01-01
Two pipeline (255,233) RS decoders, one a time domain decoder and the other a transform domain decoder, use the same first part to develop an errata locator polynomial .tau.(x), and an errata evaluator polynominal A(x). Both the time domain decoder and transform domain decoder have a modified GCD that uses an input multiplexer and an output demultiplexer to reduce the number of GCD cells required. The time domain decoder uses a Chien search and polynomial evaluator on the GCD outputs .tau.(x) and A(x), for the final decoding steps, while the transform domain decoder uses a transform error pattern algorithm operating on .tau.(x) and the initial syndrome computation S(x), followed by an inverse transform algorithm in sequence for the final decoding steps prior to adding the received RS coded message to produce a decoded output message.
Singer product apertures—A coded aperture system with a fast decoding algorithm
International Nuclear Information System (INIS)
Byard, Kevin; Shutler, Paul M.E.
2017-01-01
A new type of coded aperture configuration that enables fast decoding of the coded aperture shadowgram data is presented. Based on the products of incidence vectors generated from the Singer difference sets, we call these Singer product apertures. For a range of aperture dimensions, we compare experimentally the performance of three decoding methods: standard decoding, induction decoding and direct vector decoding. In all cases the induction and direct vector methods are several orders of magnitude faster than the standard method, with direct vector decoding being significantly faster than induction decoding. For apertures of the same dimensions the increase in speed offered by direct vector decoding over induction decoding is better for lower throughput apertures.
Singer product apertures—A coded aperture system with a fast decoding algorithm
Energy Technology Data Exchange (ETDEWEB)
Byard, Kevin, E-mail: kevin.byard@aut.ac.nz [School of Economics, Faculty of Business, Economics and Law, Auckland University of Technology, Auckland 1142 (New Zealand); Shutler, Paul M.E. [National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616 (Singapore)
2017-06-01
A new type of coded aperture configuration that enables fast decoding of the coded aperture shadowgram data is presented. Based on the products of incidence vectors generated from the Singer difference sets, we call these Singer product apertures. For a range of aperture dimensions, we compare experimentally the performance of three decoding methods: standard decoding, induction decoding and direct vector decoding. In all cases the induction and direct vector methods are several orders of magnitude faster than the standard method, with direct vector decoding being significantly faster than induction decoding. For apertures of the same dimensions the increase in speed offered by direct vector decoding over induction decoding is better for lower throughput apertures.
Research on coding and decoding method for digital levels
Energy Technology Data Exchange (ETDEWEB)
Tu Lifen; Zhong Sidong
2011-01-20
A new coding and decoding method for digital levels is proposed. It is based on an area-array CCD sensor and adopts mixed coding technology. By taking advantage of redundant information in a digital image signal, the contradiction that the field of view and image resolution restrict each other in a digital level measurement is overcome, and the geodetic leveling becomes easier. The experimental results demonstrate that the uncertainty of measurement is 1mm when the measuring range is between 2m and 100m, which can meet practical needs.
Research on coding and decoding method for digital levels.
Tu, Li-fen; Zhong, Si-dong
2011-01-20
A new coding and decoding method for digital levels is proposed. It is based on an area-array CCD sensor and adopts mixed coding technology. By taking advantage of redundant information in a digital image signal, the contradiction that the field of view and image resolution restrict each other in a digital level measurement is overcome, and the geodetic leveling becomes easier. The experimental results demonstrate that the uncertainty of measurement is 1 mm when the measuring range is between 2 m and 100 m, which can meet practical needs.
Optimized iterative decoding method for TPC coded CPM
Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei
2018-05-01
Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.
STACK DECODING OF LINEAR BLOCK CODES FOR DISCRETE MEMORYLESS CHANNEL USING TREE DIAGRAM
Directory of Open Access Journals (Sweden)
H. Prashantha Kumar
2012-03-01
Full Text Available The boundaries between block and convolutional codes have become diffused after recent advances in the understanding of the trellis structure of block codes and the tail-biting structure of some convolutional codes. Therefore, decoding algorithms traditionally proposed for decoding convolutional codes have been applied for decoding certain classes of block codes. This paper presents the decoding of block codes using tree structure. Many good block codes are presently known. Several of them have been used in applications ranging from deep space communication to error control in storage systems. But the primary difficulty with applying Viterbi or BCJR algorithms to decode of block codes is that, even though they are optimum decoding methods, the promised bit error rates are not achieved in practice at data rates close to capacity. This is because the decoding effort is fixed and grows with block length, and thus only short block length codes can be used. Therefore, an important practical question is whether a suboptimal realizable soft decision decoding method can be found for block codes. A noteworthy result which provides a partial answer to this question is described in the following sections. This result of near optimum decoding will be used as motivation for the investigation of different soft decision decoding methods for linear block codes which can lead to the development of efficient decoding algorithms. The code tree can be treated as an expanded version of the trellis, where every path is totally distinct from every other path. We have derived the tree structure for (8, 4 and (16, 11 extended Hamming codes and have succeeded in implementing the soft decision stack algorithm to decode them. For the discrete memoryless channel, gains in excess of 1.5dB at a bit error rate of 10-5 with respect to conventional hard decision decoding are demonstrated for these codes.
Linear network error correction coding
Guang, Xuan
2014-01-01
There are two main approaches in the theory of network error correction coding. In this SpringerBrief, the authors summarize some of the most important contributions following the classic approach, which represents messages by sequences?similar to algebraic coding,?and also briefly discuss the main results following the?other approach,?that uses the theory of rank metric codes for network error correction of representing messages by subspaces. This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions. Distances an
A study of the decoding of multiple pinhole coded aperture RI tomographic images
International Nuclear Information System (INIS)
Hasegawa, Takeo; Kobayashi, Akitoshi; Nishiyama, Yutaka
1980-01-01
The authors constructed a Multiple Pinhole Coded Aperture (MPCA) and developed related decoding software. When simple coordinate transformation was performed, omission of points and shifting of counts occurred. By selecting various tomographic planes and collecting count for each tomographic depth from the shadowgram, a solution to these problems was found. The counts from the central portion of the tomographic image from the MPCA were incorrectly high, this was rectified by a correction function to improve the uniformity correction program of the γ-camera. Depth resolution of the tomographic image improved in proportion to the area encompassed by the pinhole configuration. An MPCA with a uniform arrangement of pinholes (e, g, pinholes in an arrangement parallel to the X-axis or the Y-axis) yielded decoded tomographic images of inferior quality. Optimum results were obtained with a ring-shaped arrangement yielding clinically applicable tomographic images even for large objects. (author)
Indian Academy of Sciences (India)
successful consumer products of all time - the Compact Disc. (CD) digital audio .... We can make ... only 2 t additional parity check symbols are required, to be able to correct t .... display information (contah'ling music related data and a table.
Synthesizer for decoding a coded short wave length irradiation
International Nuclear Information System (INIS)
1976-01-01
The system uses point irradiation source, typically an X-ray emitter, which illuminates a three dimensional object consisting of a set of parallel planes, each of which acts as a source of coded information. The secondary source images are superimposed on a common flat screen. The decoding system comprises an imput light-screen detector, a picture screen amplifier, a beam deflector, on output picture screen, an optical focussing unit including three lenses, a masking unit, an output light screen detector and a video signal reproduction unit of cathode ray tube from, or similar, to create a three dimensional image of the object. (G.C.)
A Novel Modified Algorithm with Reduced Complexity LDPC Code Decoder
Directory of Open Access Journals (Sweden)
Song Yang
2014-10-01
Full Text Available A novel efficient decoding algorithm reduced the sum-product algorithm (SPA Complexity with LPDC code is proposed. Base on the hyperbolic tangent rule, modified the Check node update with two horizontal process, which have similar calculation, Motivated by the finding that sun- min (MS algorithm reduce the complexity reducing the approximation error in the horizontal process, simplify the information weight small part. Compared with the exiting approximations, the proposed method is less computational complexity than SPA algorithm. Simulation results show that the author algorithm can achieve performance very close SPA.
A reduced complexity highly power/bandwidth efficient coded FQPSK system with iterative decoding
Simon, M. K.; Divsalar, D.
2001-01-01
Based on a representation of FQPSK as a trellis-coded modulation, this paper investigates the potential improvement in power efficiency obtained from the application of simple outer codes to form a concatenated coding arrangement with iterative decoding.
Implementation of Layered Decoding Architecture for LDPC Code using Layered Min-Sum Algorithm
Directory of Open Access Journals (Sweden)
Sandeep Kakde
2017-12-01
Full Text Available For binary field and long code lengths, Low Density Parity Check (LDPC code approaches Shannon limit performance. LDPC codes provide remarkable error correction performance and therefore enlarge the design space for communication systems.In this paper, we have compare different digital modulation techniques and found that BPSK modulation technique is better than other modulation techniques in terms of BER. It also gives error performance of LDPC decoder over AWGN channel using Min-Sum algorithm. VLSI Architecture is proposed which uses the value re-use property of min-sum algorithm and gives high throughput. The proposed work has been implemented and tested on Xilinx Virtex 5 FPGA. The MATLAB result of LDPC decoder for low bit error rate (BER gives bit error rate in the range of 10-1 to 10-3.5 at SNR=1 to 2 for 20 no of iterations. So it gives good bit error rate performance. The latency of the parallel design of LDPC decoder has also reduced. It has accomplished 141.22 MHz maximum frequency and throughput of 2.02 Gbps while consuming less area of the design.
Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes
Lin, Shu
1998-01-01
A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and
Generalized instantly decodable network coding for relay-assisted networks
Elmahdy, Adel M.
2013-09-01
In this paper, we investigate the problem of minimizing the frame completion delay for Instantly Decodable Network Coding (IDNC) in relay-assisted wireless multicast networks. We first propose a packet recovery algorithm in the single relay topology which employs generalized IDNC instead of strict IDNC previously proposed in the literature for the same relay-assisted topology. This use of generalized IDNC is supported by showing that it is a super-set of the strict IDNC scheme, and thus can generate coding combinations that are at least as efficient as strict IDNC in reducing the average completion delay. We then extend our study to the multiple relay topology and propose a joint generalized IDNC and relay selection algorithm. This proposed algorithm benefits from the reception diversity of the multiple relays to further reduce the average completion delay in the network. Simulation results show that our proposed solutions achieve much better performance compared to previous solutions in the literature. © 2013 IEEE.
An evaluation of the effect of JPEG, JPEG2000, and H.264/AVC on CQR codes decoding process
Vizcarra Melgar, Max E.; Farias, Mylène C. Q.; Zaghetto, Alexandre
2015-02-01
This paper presents a binarymatrix code based on QR Code (Quick Response Code), denoted as CQR Code (Colored Quick Response Code), and evaluates the effect of JPEG, JPEG2000 and H.264/AVC compression on the decoding process. The proposed CQR Code has three additional colors (red, green and blue), what enables twice as much storage capacity when compared to the traditional black and white QR Code. Using the Reed-Solomon error-correcting code, the CQR Code model has a theoretical correction capability of 38.41%. The goal of this paper is to evaluate the effect that degradations inserted by common image compression algorithms have on the decoding process. Results show that a successful decoding process can be achieved for compression rates up to 0.3877 bits/pixel, 0.1093 bits/pixel and 0.3808 bits/pixel for JPEG, JPEG2000 and H.264/AVC formats, respectively. The algorithm that presents the best performance is the H.264/AVC, followed by the JPEG2000, and JPEG.
Decoding using back-project algorithm from coded image in ICF
International Nuclear Information System (INIS)
Jiang shaoen; Liu Zhongli; Zheng Zhijian; Tang Daoyuan
1999-01-01
The principle of the coded imaging and its decoding in inertial confinement fusion is described simply. The authors take ring aperture microscope for example and use back-project (BP) algorithm to decode the coded image. The decoding program has been performed for numerical simulation. Simulations of two models are made, and the results show that the accuracy of BP algorithm is high and effect of reconstruction is good. Thus, it indicates that BP algorithm is applicable to decoding for coded image in ICF experiments
Low Power LDPC Code Decoder Architecture Based on Intermediate Message Compression Technique
Shimizu, Kazunori; Togawa, Nozomu; Ikenaga, Takeshi; Goto, Satoshi
Reducing the power dissipation for LDPC code decoder is a major challenging task to apply it to the practical digital communication systems. In this paper, we propose a low power LDPC code decoder architecture based on an intermediate message-compression technique which features as follows: (i) An intermediate message compression technique enables the decoder to reduce the required memory capacity and write power dissipation. (ii) A clock gated shift register based intermediate message memory architecture enables the decoder to decompress the compressed messages in a single clock cycle while reducing the read power dissipation. The combination of the above two techniques enables the decoder to reduce the power dissipation while keeping the decoding throughput. The simulation results show that the proposed architecture improves the power efficiency up to 52% and 18% compared to that of the decoder based on the overlapped schedule and the rapid convergence schedule without the proposed techniques respectively.
Percolation bounds for decoding thresholds with correlated erasures in quantum LDPC codes
Hamilton, Kathleen; Pryadko, Leonid
Correlations between errors can dramatically affect decoding thresholds, in some cases eliminating the threshold altogether. We analyze the existence of a threshold for quantum low-density parity-check (LDPC) codes in the case of correlated erasures. When erasures are positively correlated, the corresponding multi-variate Bernoulli distribution can be modeled in terms of cluster errors, where qubits in clusters of various size can be marked all at once. In a code family with distance scaling as a power law of the code length, erasures can be always corrected below percolation on a qubit adjacency graph associated with the code. We bound this correlated percolation transition by weighted (uncorrelated) percolation on a specially constructed cluster connectivity graph, and apply our recent results to construct several bounds for the latter. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-14-1-0272.
Sheikh, Alireza; Amat, Alexandre Graell i.; Liva, Gianluigi
2017-12-01
We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \\emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \\emph{hard decision decoder} which, however, exploits \\emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \\emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.
Lei, Ted Chih-Wei; Tseng, Fan-Shuo
2017-07-01
This paper addresses the problem of high-computational complexity decoding in traditional Wyner-Ziv video coding (WZVC). The key focus is the migration of two traditionally high-computationally complex encoder algorithms, namely motion estimation and mode decision. In order to reduce the computational burden in this process, the proposed architecture adopts the partial boundary matching algorithm and four flexible types of block mode decision at the decoder. This approach does away with the need for motion estimation and mode decision at the encoder. The experimental results show that the proposed padding block-based WZVC not only decreases decoder complexity to approximately one hundredth that of the state-of-the-art DISCOVER decoding but also outperforms DISCOVER codec by up to 3 to 4 dB.
Partially blind instantly decodable network codes for lossy feedback environment
Sorour, Sameh; Douik, Ahmed S.; Valaee, Shahrokh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2014-01-01
an expression for the expected decoding delay increment for any arbitrary transmission. This expression is then used to find the optimal policy that reduces the decoding delay in such lossy feedback environment. Results show that our proposed solutions both
Row Reduction Applied to Decoding of Rank Metric and Subspace Codes
DEFF Research Database (Denmark)
Puchinger, Sven; Nielsen, Johan Sebastian Rosenkilde; Li, Wenhui
2017-01-01
We show that decoding of ℓ-Interleaved Gabidulin codes, as well as list-ℓ decoding of Mahdavifar–Vardy (MV) codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of F[x] matrices, we develop a general and flexible approach of transforming matrices over skew...... polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding ℓ-Interleaved Gabidulin codes. We obtain an algorithm with complexity O(ℓμ2) where μ measures the size of the input problem and is proportional...... to the code length n in the case of decoding. Further, we show how to perform the interpolation step of list-ℓ-decoding MV codes in complexity O(ℓn2), where n is the number of interpolation constraints....
Efficient Dual Domain Decoding of Linear Block Codes Using Genetic Algorithms
Directory of Open Access Journals (Sweden)
Ahmed Azouaoui
2012-01-01
Full Text Available A computationally efficient algorithm for decoding block codes is developed using a genetic algorithm (GA. The proposed algorithm uses the dual code in contrast to the existing genetic decoders in the literature that use the code itself. Hence, this new approach reduces the complexity of decoding the codes of high rates. We simulated our algorithm in various transmission channels. The performance of this algorithm is investigated and compared with competitor decoding algorithms including Maini and Shakeel ones. The results show that the proposed algorithm gives large gains over the Chase-2 decoding algorithm and reach the performance of the OSD-3 for some quadratic residue (QR codes. Further, we define a new crossover operator that exploits the domain specific information and compare it with uniform and two point crossover. The complexity of this algorithm is also discussed and compared to other algorithms.
VLSI Architectures for Sliding-Window-Based Space-Time Turbo Trellis Code Decoders
Directory of Open Access Journals (Sweden)
Georgios Passas
2012-01-01
Full Text Available The VLSI implementation of SISO-MAP decoders used for traditional iterative turbo coding has been investigated in the literature. In this paper, a complete architectural model of a space-time turbo code receiver that includes elementary decoders is presented. These architectures are based on newly proposed building blocks such as a recursive add-compare-select-offset (ACSO unit, A-, B-, Γ-, and LLR output calculation modules. Measurements of complexity and decoding delay of several sliding-window-technique-based MAP decoder architectures and a proposed parameter set lead to defining equations and comparison between those architectures.
Low Complexity Approach for High Throughput Belief-Propagation based Decoding of LDPC Codes
Directory of Open Access Journals (Sweden)
BOT, A.
2013-11-01
Full Text Available The paper proposes a low complexity belief propagation (BP based decoding algorithm for LDPC codes. In spite of the iterative nature of the decoding process, the proposed algorithm provides both reduced complexity and increased BER performances as compared with the classic min-sum (MS algorithm, generally used for hardware implementations. Linear approximations of check-nodes update function are used in order to reduce the complexity of the BP algorithm. Considering this decoding approach, an FPGA based hardware architecture is proposed for implementing the decoding algorithm, aiming to increase the decoder throughput. FPGA technology was chosen for the LDPC decoder implementation, due to its parallel computation and reconfiguration capabilities. The obtained results show improvements regarding decoding throughput and BER performances compared with state-of-the-art approaches.
Lee, L.-N.
1977-01-01
Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively modest coding complexity, it is proposed to concatenate a byte-oriented unit-memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real-time minimal-byte-error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.
Multi-level trellis coded modulation and multi-stage decoding
Costello, Daniel J., Jr.; Wu, Jiantian; Lin, Shu
1990-01-01
Several constructions for multi-level trellis codes are presented and many codes with better performance than previously known codes are found. These codes provide a flexible trade-off between coding gain, decoding complexity, and decoding delay. New multi-level trellis coded modulation schemes using generalized set partitioning methods are developed for Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK) signal sets. New rotationally invariant multi-level trellis codes which can be combined with differential encoding to resolve phase ambiguity are presented.
Video coding and decoding devices and methods preserving ppg relevant information
2013-01-01
The present invention relates to a video encoding device (10) for encoding video data and a corresponding video decoding device, wherein during decoding PPG relevant information shall be preserved. For this purpose the video coding device (10) comprises a first encoder (20) for encoding input video
Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes
DEFF Research Database (Denmark)
Nielsen, Johan Sebastian Rosenkilde; Zeh, Alexander
2013-01-01
An iterated refinement procedure for the Guruswami–Sudan list decoding algorithm for Generalised Reed–Solomon codes based on Alekhnovich’s module minimisation is proposed. The method is parametrisable and allows variants of the usual list decoding approach. In particular, finding the list...
Mutiple LDPC Decoding using Bitplane Correlation for Transform Domain Wyner-Ziv Video Coding
DEFF Research Database (Denmark)
Luong, Huynh Van; Huang, Xin; Forchhammer, Søren
2011-01-01
Distributed video coding (DVC) is an emerging video coding paradigm for systems which fully or partly exploit the source statistics at the decoder to reduce the computational burden at the encoder. This paper considers a Low Density Parity Check (LDPC) based Transform Domain Wyner-Ziv (TDWZ) video...... codec. To improve the LDPC coding performance in the context of TDWZ, this paper proposes a Wyner-Ziv video codec using bitplane correlation through multiple parallel LDPC decoding. The proposed scheme utilizes inter bitplane correlation to enhance the bitplane decoding performance. Experimental results...
Joint design of QC-LDPC codes for coded cooperation system with joint iterative decoding
Zhang, Shunwai; Yang, Fengfan; Tang, Lei; Ejaz, Saqib; Luo, Lin; Maharaj, B. T.
2016-03-01
In this paper, we investigate joint design of quasi-cyclic low-density-parity-check (QC-LDPC) codes for coded cooperation system with joint iterative decoding in the destination. First, QC-LDPC codes based on the base matrix and exponent matrix are introduced, and then we describe two types of girth-4 cycles in QC-LDPC codes employed by the source and relay. In the equivalent parity-check matrix corresponding to the jointly designed QC-LDPC codes employed by the source and relay, all girth-4 cycles including both type I and type II are cancelled. Theoretical analysis and numerical simulations show that the jointly designed QC-LDPC coded cooperation well combines cooperation gain and channel coding gain, and outperforms the coded non-cooperation under the same conditions. Furthermore, the bit error rate performance of the coded cooperation employing jointly designed QC-LDPC codes is better than those of random LDPC codes and separately designed QC-LDPC codes over AWGN channels.
Error Recovery Properties and Soft Decoding of Quasi-Arithmetic Codes
Directory of Open Access Journals (Sweden)
Christine Guillemot
2007-08-01
Full Text Available This paper first introduces a new set of aggregated state models for soft-input decoding of quasi arithmetic (QA codes with a termination constraint. The decoding complexity with these models is linear with the sequence length. The aggregation parameter controls the tradeoff between decoding performance and complexity. It is shown that close-to-optimal decoding performance can be obtained with low values of the aggregation parameter, that is, with a complexity which is significantly reduced with respect to optimal QA bit/symbol models. The choice of the aggregation parameter depends on the synchronization recovery properties of the QA codes. This paper thus describes a method to estimate the probability mass function (PMF of the gain/loss of symbols following a single bit error (i.e., of the difference between the number of encoded and decoded symbols. The entropy of the gain/loss turns out to be the average amount of information conveyed by a length constraint on both the optimal and aggregated state models. This quantity allows us to choose the value of the aggregation parameter that will lead to close-to-optimal decoding performance. It is shown that the optimum position for the length constraint is not the last time instant of the decoding process. This observation leads to the introduction of a new technique for robust decoding of QA codes with redundancy which turns out to outperform techniques based on the concept of forbidden symbol.
Abediseid, Walid
2012-01-01
complexity of sphere decoding for the quasi- static, lattice space-time (LAST) coded MIMO channel. Specifically, we drive an upper bound of the tail distribution of the decoder's computational complexity. We show that when the computational complexity exceeds
Machine-learning-assisted correction of correlated qubit errors in a topological code
Directory of Open Access Journals (Sweden)
Paul Baireuther
2018-01-01
Full Text Available A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X and phase-flip (Z errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.
Jointly-check iterative decoding algorithm for quantum sparse graph codes
International Nuclear Information System (INIS)
Jun-Hu, Shao; Bao-Ming, Bai; Wei, Lin; Lin, Zhou
2010-01-01
For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement. (general)
LDPC code decoding adapted to the precoded partial response magnetic recording channels
International Nuclear Information System (INIS)
Lee, Jun; Kim, Kyuyong; Lee, Jaejin; Yang, Gijoo
2004-01-01
We propose a signal processing technique using LDPC (low-density parity-check) code instead of PRML (partial response maximum likelihood) system for the longitudinal magnetic recording channel. The scheme is designed by the precoder admitting level detection at the receiver-end and modifying the likelihood function for LDPC code decoding. The scheme can be collaborated with other decoder for turbo-like systems. The proposed algorithm can contribute to improve the performance of the conventional turbo-like systems
Euclidean Geometry Codes, minimum weight words and decodable error-patterns using bit-flipping
DEFF Research Database (Denmark)
Høholdt, Tom; Justesen, Jørn; Jonsson, Bergtor
2005-01-01
We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns.......We determine the number of minimum wigth words in a class of Euclidean Geometry codes and link the performance of the bit-flipping decoding algorithm to the geometry of the error patterns....
LDPC code decoding adapted to the precoded partial response magnetic recording channels
Energy Technology Data Exchange (ETDEWEB)
Lee, Jun E-mail: leejun28@sait.samsung.co.kr; Kim, Kyuyong; Lee, Jaejin; Yang, Gijoo
2004-05-01
We propose a signal processing technique using LDPC (low-density parity-check) code instead of PRML (partial response maximum likelihood) system for the longitudinal magnetic recording channel. The scheme is designed by the precoder admitting level detection at the receiver-end and modifying the likelihood function for LDPC code decoding. The scheme can be collaborated with other decoder for turbo-like systems. The proposed algorithm can contribute to improve the performance of the conventional turbo-like systems.
Performance Analysis of Iterative Decoding Algorithms for PEG LDPC Codes in Nakagami Fading Channels
Directory of Open Access Journals (Sweden)
O. Al Rasheed
2013-11-01
Full Text Available In this paper we give a comparative analysis of decoding algorithms of Low Density Parity Check (LDPC codes in a channel with the Nakagami distribution of the fading envelope. We consider the Progressive Edge-Growth (PEG method and Improved PEG method for the parity check matrix construction, which can be used to avoid short girths, small trapping sets and a high level of error floor. A comparative analysis of several classes of LDPC codes in various propagation conditions and decoded using different decoding algorithms is also presented.
Optimized Min-Sum Decoding Algorithm for Low Density Parity Check Codes
Mohammad Rakibul Islam; Dewan Siam Shafiullah; Muhammad Mostafa Amir Faisal; Imran Rahman
2011-01-01
Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the sam...
Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
National Research Council Canada - National Science Library
Sason, Igal; Shamai, Shlomo
2006-01-01
..., upper and lower bounds on the error probability of linear codes under ML decoding are surveyed and applied to codes and ensembles of codes on graphs. For upper bounds, we discuss various bounds where focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we ad...
Jointly Decoded Raptor Codes: Analysis and Design for the BIAWGN Channel
Directory of Open Access Journals (Sweden)
Venkiah Auguste
2009-01-01
Full Text Available Abstract We are interested in the analysis and optimization of Raptor codes under a joint decoding framework, that is, when the precode and the fountain code exchange soft information iteratively. We develop an analytical asymptotic convergence analysis of the joint decoder, derive an optimization method for the design of efficient output degree distributions, and show that the new optimized distributions outperform the existing ones, both at long and moderate lengths. We also show that jointly decoded Raptor codes are robust to channel variation: they perform reasonably well over a wide range of channel capacities. This robustness property was already known for the erasure channel but not for the Gaussian channel. Finally, we discuss some finite length code design issues. Contrary to what is commonly believed, we show by simulations that using a relatively low rate for the precode , we can improve greatly the error floor performance of the Raptor code.
Fiber Bragg grating for spectral phase optical code-division multiple-access encoding and decoding
Fang, Xiaohui; Wang, Dong-Ning; Li, Shichen
2003-08-01
A new method for realizing spectral phase optical code-division multiple-access (OCDMA) coding based on step chirped fiber Bragg gratings (SCFBGs) is proposed and the corresponding encoder/decoder is presented. With this method, a mapping code is introduced for the m-sequence address code and the phase shift can be inserted into the subgratings of the SCFBG according to the mapping code. The transfer matrix method together with Fourier transform is used to investigate the characteristics of the encoder/decoder. The factors that influence the correlation property of the encoder/decoder, including index modulation and bandwidth of the subgrating, are identified. The system structure is simple and good correlation output can be obtained. The performance of the OCDMA system based on SCFBGs has been analyzed.
Complete ML Decoding orf the (73,45) PG Code
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom; Hjaltason, Johan
2005-01-01
Our recent proof of the completeness of decoding by list bit flipping is reviewed. The proof is based on an enumeration of all cosets of low weight in terms of their minimum weight and syndrome weight. By using a geometric description of the error patterns we characterize all remaining cosets....
Advanced hardware design for error correcting codes
Coussy, Philippe
2015-01-01
This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques.
Design and Analysis of Adaptive Message Coding on LDPC Decoder with Faulty Storage
Directory of Open Access Journals (Sweden)
Guangjun Ge
2018-01-01
Full Text Available Unreliable message storage severely degrades the performance of LDPC decoders. This paper discusses the impacts of message errors on LDPC decoders and schemes improving the robustness. Firstly, we develop a discrete density evolution analysis for faulty LDPC decoders, which indicates that protecting the sign bits of messages is effective enough for finite-precision LDPC decoders. Secondly, we analyze the effects of quantization precision loss for static sign bit protection and propose an embedded dynamic coding scheme by adaptively employing the least significant bits (LSBs to protect the sign bits. Thirdly, we give a construction of Hamming product code for the adaptive coding and present low complexity decoding algorithms. Theoretic analysis indicates that the proposed scheme outperforms traditional triple modular redundancy (TMR scheme in decoding both threshold and residual errors, while Monte Carlo simulations show that the performance loss is less than 0.2 dB when the storage error probability varies from 10-3 to 10-4.
Delay reduction in lossy intermittent feedback for generalized instantly decodable network coding
Douik, Ahmed S.; Sorour, Sameh; Alouini, Mohamed-Slim; Ai-Naffouri, Tareq Y.
2013-01-01
In this paper, we study the effect of lossy intermittent feedback loss events on the multicast decoding delay performance of generalized instantly decodable network coding. These feedback loss events create uncertainty at the sender about the reception statues of different receivers and thus uncertainty to accurately determine subsequent instantly decodable coded packets. To solve this problem, we first identify the different possibilities of uncertain packets at the sender and their probabilities. We then derive the expression of the mean decoding delay. We formulate the Generalized Instantly Decodable Network Coding (G-IDNC) minimum decoding delay problem as a maximum weight clique problem. Since finding the optimal solution is NP-hard, we design a variant of the algorithm employed in [1]. Our algorithm is compared to the two blind graph update proposed in [2] through extensive simulations. Results show that our algorithm outperforms the blind approaches in all the situations and achieves a tolerable degradation, against the perfect feedback, for large feedback loss period. © 2013 IEEE.
Delay reduction in lossy intermittent feedback for generalized instantly decodable network coding
Douik, Ahmed S.
2013-10-01
In this paper, we study the effect of lossy intermittent feedback loss events on the multicast decoding delay performance of generalized instantly decodable network coding. These feedback loss events create uncertainty at the sender about the reception statues of different receivers and thus uncertainty to accurately determine subsequent instantly decodable coded packets. To solve this problem, we first identify the different possibilities of uncertain packets at the sender and their probabilities. We then derive the expression of the mean decoding delay. We formulate the Generalized Instantly Decodable Network Coding (G-IDNC) minimum decoding delay problem as a maximum weight clique problem. Since finding the optimal solution is NP-hard, we design a variant of the algorithm employed in [1]. Our algorithm is compared to the two blind graph update proposed in [2] through extensive simulations. Results show that our algorithm outperforms the blind approaches in all the situations and achieves a tolerable degradation, against the perfect feedback, for large feedback loss period. © 2013 IEEE.
A Simple Scheme for Belief Propagation Decoding of BCH and RS Codes in Multimedia Transmissions
Directory of Open Access Journals (Sweden)
Marco Baldi
2008-01-01
Full Text Available Classic linear block codes, like Bose-Chaudhuri-Hocquenghem (BCH and Reed-Solomon (RS codes, are widely used in multimedia transmissions, but their soft-decision decoding still represents an open issue. Among the several approaches proposed for this purpose, an important role is played by the iterative belief propagation principle, whose application to low-density parity-check (LDPC codes permits to approach the channel capacity. In this paper, we elaborate a new technique for decoding classic binary and nonbinary codes through the belief propagation algorithm. We focus on RS codes included in the recent CDMA2000 standard, and compare the proposed technique with the adaptive belief propagation approach, that is able to ensure very good performance but with higher complexity. Moreover, we consider the case of long BCH codes included in the DVB-S2 standard, for which we show that the usage of “pure” LDPC codes would provide better performance.
Fast Transform Decoding Of Nonsystematic Reed-Solomon Codes
Truong, Trieu-Kie; Cheung, Kar-Ming; Shiozaki, A.; Reed, Irving S.
1992-01-01
Fast, efficient Fermat number transform used to compute F'(x) analogous to computation of syndrome in conventional decoding scheme. Eliminates polynomial multiplications and reduces number of multiplications in reconstruction of F'(x) to n log (n). Euclidean algorithm used to evaluate F(x) directly, without going through intermediate steps of solving error-locator and error-evaluator polynomials. Algorithm suitable for implementation in very-large-scale integrated circuits.
Fast Erasure and Error decoding of Algebraic Geometry Codes up to the Feng-Rao Bound
DEFF Research Database (Denmark)
Jensen, Helge Elbrønd; Sakata, S.; Leonard, D.
1996-01-01
This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao.......This paper gives an errata(that is erasure-and error-) decoding algorithm of one-point algebraic geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-massey algorithm and the votin procedure of Feng and Rao....
Joint Source-Channel Decoding of Variable-Length Codes with Soft Information: A Survey
Directory of Open Access Journals (Sweden)
Pierre Siohan
2005-05-01
Full Text Available Multimedia transmission over time-varying wireless channels presents a number of challenges beyond existing capabilities conceived so far for third-generation networks. Efficient quality-of-service (QoS provisioning for multimedia on these channels may in particular require a loosening and a rethinking of the layer separation principle. In that context, joint source-channel decoding (JSCD strategies have gained attention as viable alternatives to separate decoding of source and channel codes. A statistical framework based on hidden Markov models (HMM capturing dependencies between the source and channel coding components sets the foundation for optimal design of techniques of joint decoding of source and channel codes. The problem has been largely addressed in the research community, by considering both fixed-length codes (FLC and variable-length source codes (VLC widely used in compression standards. Joint source-channel decoding of VLC raises specific difficulties due to the fact that the segmentation of the received bitstream into source symbols is random. This paper makes a survey of recent theoretical and practical advances in the area of JSCD with soft information of VLC-encoded sources. It first describes the main paths followed for designing efficient estimators for VLC-encoded sources, the key component of the JSCD iterative structure. It then presents the main issues involved in the application of the turbo principle to JSCD of VLC-encoded sources as well as the main approaches to source-controlled channel decoding. This survey terminates by performance illustrations with real image and video decoding systems.
Joint Source-Channel Decoding of Variable-Length Codes with Soft Information: A Survey
Guillemot, Christine; Siohan, Pierre
2005-12-01
Multimedia transmission over time-varying wireless channels presents a number of challenges beyond existing capabilities conceived so far for third-generation networks. Efficient quality-of-service (QoS) provisioning for multimedia on these channels may in particular require a loosening and a rethinking of the layer separation principle. In that context, joint source-channel decoding (JSCD) strategies have gained attention as viable alternatives to separate decoding of source and channel codes. A statistical framework based on hidden Markov models (HMM) capturing dependencies between the source and channel coding components sets the foundation for optimal design of techniques of joint decoding of source and channel codes. The problem has been largely addressed in the research community, by considering both fixed-length codes (FLC) and variable-length source codes (VLC) widely used in compression standards. Joint source-channel decoding of VLC raises specific difficulties due to the fact that the segmentation of the received bitstream into source symbols is random. This paper makes a survey of recent theoretical and practical advances in the area of JSCD with soft information of VLC-encoded sources. It first describes the main paths followed for designing efficient estimators for VLC-encoded sources, the key component of the JSCD iterative structure. It then presents the main issues involved in the application of the turbo principle to JSCD of VLC-encoded sources as well as the main approaches to source-controlled channel decoding. This survey terminates by performance illustrations with real image and video decoding systems.
Institute of Scientific and Technical Information of China (English)
YUAN Dongfeng; WANG Chengxiang; YAO Qi; CAO Zhigang
2001-01-01
Based on "capacity rule", the perfor-mance of multilevel coding (MLC) schemes with dif-ferent set partitioning strategies and decoding meth-ods in AWGN and Rayleigh fading channels is investi-gated, in which BCH codes are chosen as componentcodes and 8ASK modulation is used. Numerical re-sults indicate that MLC scheme with UP strategy canobtain optimal performance in AWGN channels andBP is the best mapping strategy for Rayleigh fadingchannels. BP strategy is of good robustness in bothkinds of channels to realize an optimum MLC system.Multistage decoding (MSD) is a sub-optimal decodingmethod of MLC for both channels. For Ungerboeckpartitioning (UP) and mixed partitioning (MP) strat-egy, MSD is strongly recommended to use for MLCsystem, while for BP strategy, PDL is suggested to useas a simple decoding method compared with MSD.
High-Speed Soft-Decision Decoding of Two Reed-Muller Codes
Lin, Shu; Uehara, Gregory T.
1996-01-01
In his research, we have proposed the (64, 40, 8) subcode of the third-order Reed-Muller (RM) code to NASA for high-speed satellite communications. This RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. This report will summarize the key progress we have made toward achieving our eventual goal of implementing a decoder system based upon this code. In the first phase of study, we investigated the complexities of various sectionalized trellis diagrams for the proposed (64, 40, 8) RNI subcode. We found a specific 8-trellis diagram for this code which requires the least decoding complexity with a high possibility of achieving a decoding speed of 600 M bits per second (Mbps). The combination of a large number of states and a hi ch data rate will be made possible due to the utilization of a high degree of parallelism throughout the architecture. This trellis diagram will be presented and briefly described. In the second phase of study which was carried out through the past year, we investigated circuit architectures to determine the feasibility of VLSI implementation of a high-speed Viterbi decoder based on this 8-section trellis diagram. We began to examine specific design and implementation approaches to implement a fully custom integrated circuit (IC) which will be a key building block for a decoder system implementation. The key results will be presented in this report. This report will be divided into three primary sections. First, we will briefly describe the system block diagram in which the proposed decoder is assumed to be operating and present some of the key architectural approaches being used to
A lossy graph model for delay reduction in generalized instantly decodable network coding
Douik, Ahmed S.
2014-06-01
The problem of minimizing the decoding delay in Generalized instantly decodable network coding (G-IDNC) for both perfect and lossy feedback scenarios is formulated as a maximum weight clique problem over the G-IDNC graph in. In this letter, we introduce a new lossy G-IDNC graph (LG-IDNC) model to further minimize the decoding delay in lossy feedback scenarios. Whereas the G-IDNC graph represents only doubtless combinable packets, the LG-IDNC graph represents also uncertain packet combinations, arising from lossy feedback events, when the expected decoding delay of XORing them among themselves or with other certain packets is lower than that expected when sending these packets separately. We compare the decoding delay performance of LG-IDNC and G-IDNC graphs through extensive simulations. Numerical results show that our new LG-IDNC graph formulation outperforms the G-IDNC graph formulation in all lossy feedback situations and achieves significant improvement in the decoding delay especially when the feedback erasure probability is higher than the packet erasure probability. © 2012 IEEE.
Abediseid, Walid
2012-12-21
The exact average complexity analysis of the basic sphere decoder for general space-time codes applied to multiple-input multiple-output (MIMO) wireless channel is known to be difficult. In this work, we shed the light on the computational complexity of sphere decoding for the quasi- static, lattice space-time (LAST) coded MIMO channel. Specifically, we drive an upper bound of the tail distribution of the decoder\\'s computational complexity. We show that when the computational complexity exceeds a certain limit, this upper bound becomes dominated by the outage probability achieved by LAST coding and sphere decoding schemes. We then calculate the minimum average computational complexity that is required by the decoder to achieve near optimal performance in terms of the system parameters. Our results indicate that there exists a cut-off rate (multiplexing gain) for which the average complexity remains bounded. Copyright © 2012 John Wiley & Sons, Ltd.
Non-binary Hybrid LDPC Codes: Structure, Decoding and Optimization
Sassatelli, Lucile; Declercq, David
2007-01-01
In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques exist for binary LDPC codes and more recently for non-binary LDPC codes, they both exhibit drawbacks due to different reasons. Our goal is to capitalize on the advantages of both families by building codes with binary (or small finite set order) and non-bin...
Coding for Parallel Links to Maximize the Expected Value of Decodable Messages
Klimesh, Matthew A.; Chang, Christopher S.
2011-01-01
When multiple parallel communication links are available, it is useful to consider link-utilization strategies that provide tradeoffs between reliability and throughput. Interesting cases arise when there are three or more available links. Under the model considered, the links have known probabilities of being in working order, and each link has a known capacity. The sender has a number of messages to send to the receiver. Each message has a size and a value (i.e., a worth or priority). Messages may be divided into pieces arbitrarily, and the value of each piece is proportional to its size. The goal is to choose combinations of messages to send on the links so that the expected value of the messages decodable by the receiver is maximized. There are three parts to the innovation: (1) Applying coding to parallel links under the model; (2) Linear programming formulation for finding the optimal combinations of messages to send on the links; and (3) Algorithms for assisting in finding feasible combinations of messages, as support for the linear programming formulation. There are similarities between this innovation and methods developed in the field of network coding. However, network coding has generally been concerned with either maximizing throughput in a fixed network, or robust communication of a fixed volume of data. In contrast, under this model, the throughput is expected to vary depending on the state of the network. Examples of error-correcting codes that are useful under this model but which are not needed under previous models have been found. This model can represent either a one-shot communication attempt, or a stream of communications. Under the one-shot model, message sizes and link capacities are quantities of information (e.g., measured in bits), while under the communications stream model, message sizes and link capacities are information rates (e.g., measured in bits/second). This work has the potential to increase the value of data returned from
Performance Analysis of Faulty Gallager-B Decoding of QC-LDPC Codes with Applications
Directory of Open Access Journals (Sweden)
O. Al Rasheed
2014-06-01
Full Text Available In this paper we evaluate the performance of Gallager-B algorithm, used for decoding low-density parity-check (LDPC codes, under unreliable message computation. Our analysis is restricted to LDPC codes constructed from circular matrices (QC-LDPC codes. Using Monte Carlo simulation we investigate the effects of different code parameters on coding system performance, under a binary symmetric communication channel and independent transient faults model. One possible application of the presented analysis in designing memory architecture with unreliable components is considered.
Simulation of Hamming Coding and Decoding for Microcontroller Radiation Hardening
Rehab I. Abdul Rahman; Mazhar B. Tayel
2015-01-01
This paper presents a method of hardening the 8051 micro-controller, able to assure reliable operation in the presence of bit flips caused by radiation. Aiming at avoiding such faults in the 8051 micro-controller, Hamming code protection was used in its SRAM memory and registers. A VHDL code has been used for this hamming code protection.
Channel coding/decoding alternatives for compressed TV data on advanced planetary missions.
Rice, R. F.
1972-01-01
The compatibility of channel coding/decoding schemes with a specific TV compressor developed for advanced planetary missions is considered. Under certain conditions, it is shown that compressed data can be transmitted at approximately the same rate as uncompressed data without any loss in quality. Thus, the full gains of data compression can be achieved in real-time transmission.
Decoding Different Patterns in Various Grey Tones Incorporated in the QR Code
Directory of Open Access Journals (Sweden)
Filip Cvitić
2014-07-01
Full Text Available Using colors in bar codes causes errors that may adversely affect their readability (Tan etal. 2010, given that the contrast between data and background modules is reduced. Due to the unreliability of using color bar codes, most designers still keep to the limitations placed by Pira International (Smithers Pira in 2002 (Williams, 2004. Since the contrast between data modules and background modules is the most important aspect in the process of reliable bar code decoding, this paper explores the dependence of reliable decoding of QR codes incorporated with combinations of grey tones on the technical characteristics of the cameras on smartphones that were marketed in the period between 2008 and 2012.
Directory of Open Access Journals (Sweden)
H. Prashantha Kumar
2011-09-01
Full Text Available Low density parity check (LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical Shannon limit for a memory less channel. LDPC codes are finding increasing use in applications like LTE-Networks, digital television, high density data storage systems, deep space communication systems etc. Several algebraic and combinatorial methods are available for constructing LDPC codes. In this paper we discuss a novel low complexity algebraic method for constructing regular LDPC like codes derived from full rank codes. We demonstrate that by employing these codes over AWGN channels, coding gains in excess of 2dB over un-coded systems can be realized when soft iterative decoding using a parity check tree is employed.
Research on the coding and decoding technology of the OCDMA system
Li, Ping; Wang, Yuru; Lan, Zhenping; Wang, Jinpeng; Zou, Nianyu
2015-12-01
Optical Code Division Multiplex Access, OCDMA, is a kind of new technology which is combined the wireless CDMA technology and the optical fiber communication technology together. The address coding technology in OCDMA system has been researched. Besides, the principle of the codec based on optical fiber delay line and non-coherent spectral domain encoding and decoding has been introduced and analysed, and the results was verified by experiment.
Liu, K. Y.
1986-01-01
High-speed decoder intended for use with Reed-Solomon (RS) codes of long code length and high error-correcting capability. Design based on algorithm that includes high-radix Fermat transform procedure, which is most efficient for high speeds. RS code in question has code-word length of 256 symbols, of which 224 are information symbols and 32 are redundant.
D-DSC: Decoding Delay-based Distributed Source Coding for Internet of Sensing Things.
Aktas, Metin; Kuscu, Murat; Dinc, Ergin; Akan, Ozgur B
2018-01-01
Spatial correlation between densely deployed sensor nodes in a wireless sensor network (WSN) can be exploited to reduce the power consumption through a proper source coding mechanism such as distributed source coding (DSC). In this paper, we propose the Decoding Delay-based Distributed Source Coding (D-DSC) to improve the energy efficiency of the classical DSC by employing the decoding delay concept which enables the use of the maximum correlated portion of sensor samples during the event estimation. In D-DSC, network is partitioned into clusters, where the clusterheads communicate their uncompressed samples carrying the side information, and the cluster members send their compressed samples. Sink performs joint decoding of the compressed and uncompressed samples and then reconstructs the event signal using the decoded sensor readings. Based on the observed degree of the correlation among sensor samples, the sink dynamically updates and broadcasts the varying compression rates back to the sensor nodes. Simulation results for the performance evaluation reveal that D-DSC can achieve reliable and energy-efficient event communication and estimation for practical signal detection/estimation applications having massive number of sensors towards the realization of Internet of Sensing Things (IoST).
Continuous-variable quantum erasure correcting code
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Sabuncu, Metin; Huck, Alexander
2010-01-01
We experimentally demonstrate a continuous variable quantum erasure-correcting code, which protects coherent states of light against complete erasure. The scheme encodes two coherent states into a bi-party entangled state, and the resulting 4-mode code is conveyed through 4 independent channels...
Performance of Product Codes and Related Structures with Iterated Decoding
DEFF Research Database (Denmark)
Justesen, Jørn
2011-01-01
Several modifications of product codes have been suggested as standards for optical networks. We show that the performance exhibits a threshold that can be estimated from a result about random graphs. For moderate input bit error probabilities, the output error rates for codes of finite length can...
Method and device for decoding coded digital video signals
2000-01-01
The invention relates to a video coding method and system including a quantization and coding sub-assembly (38) in which a quantization parameter is controlled by another parameter defined as being in direct relation with the dynamic range value of the data contained in given blocks of pixels.
Iterated decoding of modified product codes in optical networks
DEFF Research Database (Denmark)
Justesen, Jørn
2009-01-01
Appendix I of the standard ITU-T G.975 contains several codes that have been proposed for improved performance of optical transmission. While the original application was submarine cables, the codes are now also used in terrestrial systems where wavelength-division multiplexing (WDM) is introduced...
Blind Decoding of Multiple Description Codes over OFDM Systems via Sequential Monte Carlo
Directory of Open Access Journals (Sweden)
Guo Dong
2005-01-01
Full Text Available We consider the problem of transmitting a continuous source through an OFDM system. Multiple description scalar quantization (MDSQ is applied to the source signal, resulting in two correlated source descriptions. The two descriptions are then OFDM modulated and transmitted through two parallel frequency-selective fading channels. At the receiver, a blind turbo receiver is developed for joint OFDM demodulation and MDSQ decoding. Transformation of the extrinsic information of the two descriptions are exchanged between each other to improve system performance. A blind soft-input soft-output OFDM detector is developed, which is based on the techniques of importance sampling and resampling. Such a detector is capable of exchanging the so-called extrinsic information with the other component in the above turbo receiver, and successively improving the overall receiver performance. Finally, we also treat channel-coded systems, and a novel blind turbo receiver is developed for joint demodulation, channel decoding, and MDSQ source decoding.
Product code optimization for determinate state LDPC decoding in robust image transmission.
Thomos, Nikolaos; Boulgouris, Nikolaos V; Strintzis, Michael G
2006-08-01
We propose a novel scheme for error-resilient image transmission. The proposed scheme employs a product coder consisting of low-density parity check (LDPC) codes and Reed-Solomon codes in order to deal effectively with bit errors. The efficiency of the proposed scheme is based on the exploitation of determinate symbols in Tanner graph decoding of LDPC codes and a novel product code optimization technique based on error estimation. Experimental evaluation demonstrates the superiority of the proposed system in comparison to recent state-of-the-art techniques for image transmission.
Douik, Ahmed S.
2015-11-05
This paper considers the multicast decoding delay reduction problem for generalized instantly decodable network coding (G-IDNC) over persistent erasure channels with feedback imperfections. The feedback scenario discussed is the most general situation in which the sender does not always receive acknowledgments from the receivers after each transmission and the feedback communications are subject to loss. The decoding delay increment expressions are derived and employed to express the decoding delay reduction problem as a maximum weight clique problem in the G-IDNC graph. This paper provides a theoretical analysis of the expected decoding delay increase at each time instant. Problem formulations in simpler channel and feedback models are shown to be special cases of the proposed generalized formulation. Since finding the optimal solution to the problem is known to be NP-hard, a suboptimal greedy algorithm is designed and compared with blind approaches proposed in the literature. Through extensive simulations, the proposed algorithm is shown to outperform the blind methods in all situations and to achieve significant improvement, particularly for high time-correlated channels.
Analysis of error floor of LDPC codes under LP decoding over the BSC
Energy Technology Data Exchange (ETDEWEB)
Chertkov, Michael [Los Alamos National Laboratory; Chilappagari, Shashi [UNIV OF AZ; Vasic, Bane [UNIV OF AZ; Stepanov, Mikhail [UNIV OF AZ
2009-01-01
We consider linear programming (LP) decoding of a fixed low-density parity-check (LDPC) code over the binary symmetric channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We propose an efficient algorithm termed the instanton search algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton and prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of flips in the input. We obtain the number of unique instantons of different sizes by running the ISA sufficient number of times. We then use the instanton statistics to predict the performance of the LP decoding over the BSC in the error floor region. We also propose an efficient semi-analytical method to predict the performance of LP decoding over a large range of transition probabilities of the BSC.
Douik, Ahmed S.; Sorour, Sameh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2015-01-01
This paper considers the multicast decoding delay reduction problem for generalized instantly decodable network coding (G-IDNC) over persistent erasure channels with feedback imperfections. The feedback scenario discussed is the most general situation in which the sender does not always receive acknowledgments from the receivers after each transmission and the feedback communications are subject to loss. The decoding delay increment expressions are derived and employed to express the decoding delay reduction problem as a maximum weight clique problem in the G-IDNC graph. This paper provides a theoretical analysis of the expected decoding delay increase at each time instant. Problem formulations in simpler channel and feedback models are shown to be special cases of the proposed generalized formulation. Since finding the optimal solution to the problem is known to be NP-hard, a suboptimal greedy algorithm is designed and compared with blind approaches proposed in the literature. Through extensive simulations, the proposed algorithm is shown to outperform the blind methods in all situations and to achieve significant improvement, particularly for high time-correlated channels.
Decoding the function of nuclear long non-coding RNAs.
Chen, Ling-Ling; Carmichael, Gordon G
2010-06-01
Long non-coding RNAs (lncRNAs) are mRNA-like, non-protein-coding RNAs that are pervasively transcribed throughout eukaryotic genomes. Rather than silently accumulating in the nucleus, many of these are now known or suspected to play important roles in nuclear architecture or in the regulation of gene expression. In this review, we highlight some recent progress in how lncRNAs regulate these important nuclear processes at the molecular level. Copyright 2010 Elsevier Ltd. All rights reserved.
Joint Coding/Decoding for Multi-message HARQ
Benyouss , Abdellatif; Jabi , Mohammed; Le Treust , Maël; Szczecinski , Leszek
2016-01-01
International audience; In this work, we propose and investigate a new coding strategy devised to increase the throughput of hybrid ARQ (HARQ) transmission over block fading channel. In our proposition, the transmitter jointly encodes a variable number of bits for each round of HARQ. The parameters (rates) of this joint coding can vary and may be based on the negative acknowledgment (NACK) signals provided by the receiver or, on the past (outdated) information about the channel states. The re...
A Dual Coding Theoretical Model of Decoding in Reading: Subsuming the LaBerge and Samuels Model
Sadoski, Mark; McTigue, Erin M.; Paivio, Allan
2012-01-01
In this article we present a detailed Dual Coding Theory (DCT) model of decoding. The DCT model reinterprets and subsumes The LaBerge and Samuels (1974) model of the reading process which has served well to account for decoding behaviors and the processes that underlie them. However, the LaBerge and Samuels model has had little to say about…
A Unique Perspective on Data Coding and Decoding
Directory of Open Access Journals (Sweden)
Wen-Yan Wang
2010-12-01
Full Text Available The concept of a loss-less data compression coding method is proposed, and a detailed description of each of its steps follows. Using the Calgary Corpus and Wikipedia data as the experimental samples and compared with existing algorithms, like PAQ or PPMstr, the new coding method could not only compress the source data, but also further re-compress the data produced by the other compression algorithms. The final files are smaller, and by comparison with the original compression ratio, at least 1% redundancy could be eliminated. The new method is simple and easy to realize. Its theoretical foundation is currently under study. The corresponding Matlab source code is provided in the Appendix.
Construction and Iterative Decoding of LDPC Codes Over Rings for Phase-Noisy Channels
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William G. Cowley
2008-04-01
Full Text Available This paper presents the construction and iterative decoding of low-density parity-check (LDPC codes for channels affected by phase noise. The LDPC code is based on integer rings and designed to converge under phase-noisy channels. We assume that phase variations are small over short blocks of adjacent symbols. A part of the constructed code is inherently built with this knowledge and hence able to withstand a phase rotation of 2ÃÂ€/M radians, where Ã¢Â€ÂœMÃ¢Â€Â is the number of phase symmetries in the signal set, that occur at different observation intervals. Another part of the code estimates the phase ambiguity present in every observation interval. The code makes use of simple blind or turbo phase estimators to provide phase estimates over every observation interval. We propose an iterative decoding schedule to apply the sum-product algorithm (SPA on the factor graph of the code for its convergence. To illustrate the new method, we present the performance results of an LDPC code constructed over Ã¢Â„Â¤4 with quadrature phase shift keying (QPSK modulated signals transmitted over a static channel, but affected by phase noise, which is modeled by the Wiener (random-walk process. The results show that the code can withstand phase noise of 2Ã¢ÂˆÂ˜ standard deviation per symbol with small loss.
Construction and Iterative Decoding of LDPC Codes Over Rings for Phase-Noisy Channels
Directory of Open Access Journals (Sweden)
Karuppasami Sridhar
2008-01-01
Full Text Available Abstract This paper presents the construction and iterative decoding of low-density parity-check (LDPC codes for channels affected by phase noise. The LDPC code is based on integer rings and designed to converge under phase-noisy channels. We assume that phase variations are small over short blocks of adjacent symbols. A part of the constructed code is inherently built with this knowledge and hence able to withstand a phase rotation of radians, where " " is the number of phase symmetries in the signal set, that occur at different observation intervals. Another part of the code estimates the phase ambiguity present in every observation interval. The code makes use of simple blind or turbo phase estimators to provide phase estimates over every observation interval. We propose an iterative decoding schedule to apply the sum-product algorithm (SPA on the factor graph of the code for its convergence. To illustrate the new method, we present the performance results of an LDPC code constructed over with quadrature phase shift keying (QPSK modulated signals transmitted over a static channel, but affected by phase noise, which is modeled by the Wiener (random-walk process. The results show that the code can withstand phase noise of standard deviation per symbol with small loss.
Threshold Multi Split-Row algorithm for decoding irregular LDPC codes
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Chakir Aqil
2017-12-01
Full Text Available In this work, we propose a new threshold multi split-row algorithm in order to improve the multi split-row algorithm for LDPC irregular codes decoding. We give a complete description of our algorithm as well as its advantages for the LDPC codes. The simulation results over an additive white gaussian channel show that an improvement in code error performance between 0.4 dB and 0.6 dB compared to the multi split-row algorithm.
Polynomial theory of error correcting codes
Cancellieri, Giovanni
2015-01-01
The book offers an original view on channel coding, based on a unitary approach to block and convolutional codes for error correction. It presents both new concepts and new families of codes. For example, lengthened and modified lengthened cyclic codes are introduced as a bridge towards time-invariant convolutional codes and their extension to time-varying versions. The novel families of codes include turbo codes and low-density parity check (LDPC) codes, the features of which are justified from the structural properties of the component codes. Design procedures for regular LDPC codes are proposed, supported by the presented theory. Quasi-cyclic LDPC codes, in block or convolutional form, represent one of the most original contributions of the book. The use of more than 100 examples allows the reader gradually to gain an understanding of the theory, and the provision of a list of more than 150 definitions, indexed at the end of the book, permits rapid location of sought information.
Decoding the non-coding RNAs in Alzheimer's disease.
Schonrock, Nicole; Götz, Jürgen
2012-11-01
Non-coding RNAs (ncRNAs) are integral components of biological networks with fundamental roles in regulating gene expression. They can integrate sequence information from the DNA code, epigenetic regulation and functions of multimeric protein complexes to potentially determine the epigenetic status and transcriptional network in any given cell. Humans potentially contain more ncRNAs than any other species, especially in the brain, where they may well play a significant role in human development and cognitive ability. This review discusses their emerging role in Alzheimer's disease (AD), a human pathological condition characterized by the progressive impairment of cognitive functions. We discuss the complexity of the ncRNA world and how this is reflected in the regulation of the amyloid precursor protein and Tau, two proteins with central functions in AD. By understanding this intricate regulatory network, there is hope for a better understanding of disease mechanisms and ultimately developing diagnostic and therapeutic tools.
Biometrics encryption combining palmprint with two-layer error correction codes
Li, Hengjian; Qiu, Jian; Dong, Jiwen; Feng, Guang
2017-07-01
To bridge the gap between the fuzziness of biometrics and the exactitude of cryptography, based on combining palmprint with two-layer error correction codes, a novel biometrics encryption method is proposed. Firstly, the randomly generated original keys are encoded by convolutional and cyclic two-layer coding. The first layer uses a convolution code to correct burst errors. The second layer uses cyclic code to correct random errors. Then, the palmprint features are extracted from the palmprint images. Next, they are fused together by XORing operation. The information is stored in a smart card. Finally, the original keys extraction process is the information in the smart card XOR the user's palmprint features and then decoded with convolutional and cyclic two-layer code. The experimental results and security analysis show that it can recover the original keys completely. The proposed method is more secure than a single password factor, and has higher accuracy than a single biometric factor.
Delay reduction in persistent erasure channels for generalized instantly decodable network coding
Sorour, Sameh
2013-06-01
In this paper, we consider the problem of minimizing the decoding delay of generalized instantly decodable network coding (G-IDNC) in persistent erasure channels (PECs). By persistent erasure channels, we mean erasure channels with memory, which are modeled as a Gilbert-Elliott two-state Markov model with good and bad channel states. In this scenario, the channel erasure dependence, represented by the transition probabilities of this channel model, is an important factor that could be exploited to reduce the decoding delay. We first formulate the G-IDNC minimum decoding delay problem in PECs as a maximum weight clique problem over the G-IDNC graph. Since finding the optimal solution of this formulation is NP-hard, we propose two heuristic algorithms to solve it and compare them using extensive simulations. Simulation results show that each of these heuristics outperforms the other in certain ranges of channel memory levels. They also show that the proposed heuristics significantly outperform both the optimal strict IDNC in the literature and the channel-unaware G-IDNC algorithms. © 2013 IEEE.
Delay reduction in persistent erasure channels for generalized instantly decodable network coding
Sorour, Sameh; Aboutorab, Neda; Sadeghi, Parastoo; Karim, Mohammad Shahriar; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2013-01-01
In this paper, we consider the problem of minimizing the decoding delay of generalized instantly decodable network coding (G-IDNC) in persistent erasure channels (PECs). By persistent erasure channels, we mean erasure channels with memory, which are modeled as a Gilbert-Elliott two-state Markov model with good and bad channel states. In this scenario, the channel erasure dependence, represented by the transition probabilities of this channel model, is an important factor that could be exploited to reduce the decoding delay. We first formulate the G-IDNC minimum decoding delay problem in PECs as a maximum weight clique problem over the G-IDNC graph. Since finding the optimal solution of this formulation is NP-hard, we propose two heuristic algorithms to solve it and compare them using extensive simulations. Simulation results show that each of these heuristics outperforms the other in certain ranges of channel memory levels. They also show that the proposed heuristics significantly outperform both the optimal strict IDNC in the literature and the channel-unaware G-IDNC algorithms. © 2013 IEEE.
Directory of Open Access Journals (Sweden)
Rovini Massimo
2009-01-01
Full Text Available This is a reply to the comments by Gunnam et al. "Comments on 'Techniques and architectures for hazard-free semi-parallel decoding of LDPC codes'", EURASIP Journal on Embedded Systems, vol. 2009, Article ID 704174 on our recent work "Techniques and architectures for hazard-free semi-parallel decoding of LDPC codes", EURASIP Journal on Embedded Systems, vol. 2009, Article ID 723465.
NONCODE v2.0: decoding the non-coding.
He, Shunmin; Liu, Changning; Skogerbø, Geir; Zhao, Haitao; Wang, Jie; Liu, Tao; Bai, Baoyan; Zhao, Yi; Chen, Runsheng
2008-01-01
The NONCODE database is an integrated knowledge database designed for the analysis of non-coding RNAs (ncRNAs). Since NONCODE was first released 3 years ago, the number of known ncRNAs has grown rapidly, and there is growing recognition that ncRNAs play important regulatory roles in most organisms. In the updated version of NONCODE (NONCODE v2.0), the number of collected ncRNAs has reached 206 226, including a wide range of microRNAs, Piwi-interacting RNAs and mRNA-like ncRNAs. The improvements brought to the database include not only new and updated ncRNA data sets, but also an incorporation of BLAST alignment search service and access through our custom UCSC Genome Browser. NONCODE can be found under http://www.noncode.org or http://noncode.bioinfo.org.cn.
Flavivirus RNAi suppression: decoding non-coding RNA.
Pijlman, Gorben P
2014-08-01
Flaviviruses are important human pathogens that are transmitted by invertebrate vectors, mostly mosquitoes and ticks. During replication in their vector, flaviviruses are subject to a potent innate immune response known as antiviral RNA interference (RNAi). This defense mechanism is associated with the production of small interfering (si)RNA that lead to degradation of viral RNA. To what extent flaviviruses would benefit from counteracting antiviral RNAi is subject of debate. Here, the experimental evidence to suggest the existence of flavivirus RNAi suppressors is discussed. I will highlight the putative role of non-coding, subgenomic flavivirus RNA in suppression of RNAi in insect and mammalian cells. Novel insights from ongoing research will reveal how arthropod-borne viruses modulate innate immunity including antiviral RNAi. Copyright © 2014 Elsevier B.V. All rights reserved.
Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators
Niu, Murphy Yuezhen; Chuang, Isaac L.; Shapiro, Jeffrey H.
2018-03-01
We establish a symmetry-operator framework for designing quantum error-correcting (QEC) codes based on fundamental properties of the underlying system dynamics. Based on this framework, we propose three hardware-efficient bosonic QEC codes that are suitable for χ(2 )-interaction based quantum computation in multimode Fock bases: the χ(2 ) parity-check code, the χ(2 ) embedded error-correcting code, and the χ(2 ) binomial code. All of these QEC codes detect photon-loss or photon-gain errors by means of photon-number parity measurements, and then correct them via χ(2 ) Hamiltonian evolutions and linear-optics transformations. Our symmetry-operator framework provides a systematic procedure for finding QEC codes that are not stabilizer codes, and it enables convenient extension of a given encoding to higher-dimensional qudit bases. The χ(2 ) binomial code is of special interest because, with m ≤N identified from channel monitoring, it can correct m -photon-loss errors, or m -photon-gain errors, or (m -1 )th -order dephasing errors using logical qudits that are encoded in O (N ) photons. In comparison, other bosonic QEC codes require O (N2) photons to correct the same degree of bosonic errors. Such improved photon efficiency underscores the additional error-correction power that can be provided by channel monitoring. We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ(2 ) parity-check code and the χ(2 ) embedded error-correcting code, and we prove that these codes saturate their respective bounds. Our χ(2 ) QEC codes exhibit hardware efficiency in that they address the principal error mechanisms and exploit the available physical interactions of the underlying hardware, thus reducing the physical resources required for implementing their encoding, decoding, and error-correction operations, and their universal encoded-basis gate sets.
Population coding and decoding in a neural field: a computational study.
Wu, Si; Amari, Shun-Ichi; Nakahara, Hiroyuki
2002-05-01
This study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable. A general prototype model for the encoding process is proposed, in which neural responses are correlated, with strength specified by a gaussian function of their difference in preferred stimuli. Based on the model, we study the effect of correlation on the Fisher information, compare the performances of three decoding methods that differ in the amount of encoding information being used, and investigate the implementation of the three methods by using a recurrent network. This study not only rediscovers main results in existing literatures in a unified way, but also reveals important new features, especially when the neural correlation is strong. As the neural correlation of firing becomes larger, the Fisher information decreases drastically. We confirm that as the width of correlation increases, the Fisher information saturates and no longer increases in proportion to the number of neurons. However, we prove that as the width increases further--wider than (sqrt)2 times the effective width of the turning function--the Fisher information increases again, and it increases without limit in proportion to the number of neurons. Furthermore, we clarify the asymptotic efficiency of the maximum likelihood inference (MLI) type of decoding methods for correlated neural signals. It shows that when the correlation covers a nonlocal range of population (excepting the uniform correlation and when the noise is extremely small), the MLI type of method, whose decoding error satisfies the Cauchy-type distribution, is not asymptotically efficient. This implies that the variance is no longer adequate to measure decoding accuracy.
Coding and decoding in a point-to-point communication using the polarization of the light beam.
Kavehvash, Z; Massoumian, F
2008-05-10
A new technique for coding and decoding of optical signals through the use of polarization is described. In this technique the concept of coding is translated to polarization. In other words, coding is done in such a way that each code represents a unique polarization. This is done by implementing a binary pattern on a spatial light modulator in such a way that the reflected light has the required polarization. Decoding is done by the detection of the received beam's polarization. By linking the concept of coding to polarization we can use each of these concepts in measuring the other one, attaining some gains. In this paper the construction of a simple point-to-point communication where coding and decoding is done through polarization will be discussed.
Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications
Douik, Ahmed S.
2015-05-01
From its introduction to its quindecennial, network coding have built a strong reputation in enhancing packet recovery process and achieving maximum information flow in both wires and wireless networks. Traditional studies focused on optimizing the throughput of the network by proposing complex schemes that achieve optimal delay. With the shift toward distributed computing at mobile devices, throughput and complexity become both critical factors that affect the efficiency of a coding scheme. Instantly decodable network coding imposed itself as a new paradigm in network coding that trades off this two aspects. This paper presents a survey of instantly decodable network coding schemes that are proposed in the literature. The various schemes are identified, categorized and evaluated. Two categories can be distinguished namely the conventional centralized schemes and the distributed or cooperative schemes. For each scheme, the comparison is carried out in terms of reliability, performance, complexity and packet selection methodology. Although the performance is generally inversely proportional to the computation complexity, numerous successful schemes from both the performance and complexity viewpoint are identified.
Instantly Decodable Network Coding: From Centralized to Device-to-Device Communications
Douik, Ahmed S.
2015-01-01
From its introduction to its quindecennial, network coding have built a strong reputation in enhancing packet recovery process and achieving maximum information flow in both wires and wireless networks. Traditional studies focused on optimizing the throughput of the network by proposing complex schemes that achieve optimal delay. With the shift toward distributed computing at mobile devices, throughput and complexity become both critical factors that affect the efficiency of a coding scheme. Instantly decodable network coding imposed itself as a new paradigm in network coding that trades off this two aspects. This paper presents a survey of instantly decodable network coding schemes that are proposed in the literature. The various schemes are identified, categorized and evaluated. Two categories can be distinguished namely the conventional centralized schemes and the distributed or cooperative schemes. For each scheme, the comparison is carried out in terms of reliability, performance, complexity and packet selection methodology. Although the performance is generally inversely proportional to the computation complexity, numerous successful schemes from both the performance and complexity viewpoint are identified.
The "periodic table" of the genetic code: A new way to look at the code and the decoding process.
Komar, Anton A
2016-01-01
Henri Grosjean and Eric Westhof recently presented an information-rich, alternative view of the genetic code, which takes into account current knowledge of the decoding process, including the complex nature of interactions between mRNA, tRNA and rRNA that take place during protein synthesis on the ribosome, and it also better reflects the evolution of the code. The new asymmetrical circular genetic code has a number of advantages over the traditional codon table and the previous circular diagrams (with a symmetrical/clockwise arrangement of the U, C, A, G bases). Most importantly, all sequence co-variances can be visualized and explained based on the internal logic of the thermodynamics of codon-anticodon interactions.
Naud, Richard; Gerstner, Wulfram
2012-01-01
The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a 'quasi-renewal equation' which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.
Zhang, Xu; Wang, Fengshan; Sheng, Juzheng
2016-06-16
Heparan sulfate (HS) is widely distributed in mammalian tissues in the form of HS proteoglycans, which play essential roles in various physiological and pathological processes. In contrast to the template-guided processes involved in the synthesis of DNA and proteins, HS biosynthesis is not believed to involve a template. However, it appears that the final structure of HS chains was strictly regulated. Herein, we report research based hypothesis that two major steps, namely "coding" and "decoding" steps, are involved in the biosynthesis of HS, which strictly regulate its chemical structure and biological activity. The "coding" process in this context is based on the distribution of sulfate moieties on the amino groups of the glucosamine residues in the HS chains. The sulfation of these amine groups is catalyzed by N-deacetylase/N-sulfotransferase, which has four isozymes. The composition and distribution of sulfate groups and iduronic acid residues on the glycan chains of HS are determined by several other modification enzymes, which can recognize these coding sequences (i.e., the "decoding" process). The degree and pattern of the sulfation and epimerization in the HS chains determines the extent of their interactions with several different protein factors, which further influences their biological activity. Copyright © 2016 Elsevier Ltd. All rights reserved.
Wittevrongel, Benjamin; Van Wolputte, Elia; Van Hulle, Marc M
2017-11-08
When encoding visual targets using various lagged versions of a pseudorandom binary sequence of luminance changes, the EEG signal recorded over the viewer's occipital pole exhibits so-called code-modulated visual evoked potentials (cVEPs), the phase lags of which can be tied to these targets. The cVEP paradigm has enjoyed interest in the brain-computer interfacing (BCI) community for the reported high information transfer rates (ITR, in bits/min). In this study, we introduce a novel decoding algorithm based on spatiotemporal beamforming, and show that this algorithm is able to accurately identify the gazed target. Especially for a small number of repetitions of the coding sequence, our beamforming approach significantly outperforms an optimised support vector machine (SVM)-based classifier, which is considered state-of-the-art in cVEP-based BCI. In addition to the traditional 60 Hz stimulus presentation rate for the coding sequence, we also explore the 120 Hz rate, and show that the latter enables faster communication, with a maximal median ITR of 172.87 bits/min. Finally, we also report on a transition effect in the EEG signal following the onset of the stimulus sequence, and recommend to exclude the first 150 ms of the trials from decoding when relying on a single presentation of the stimulus sequence.
Directory of Open Access Journals (Sweden)
Savitha H. M.
2010-09-01
Full Text Available A comparison of the performance of hard and soft-decision turbo coded Orthogonal Frequency Division Multiplexing systems with Quadrature Phase Shift Keying (QPSK and 16-Quadrature Amplitude Modulation (16-QAM is considered in the first section of this paper. The results show that the soft-decision method greatly outperforms the hard-decision method. The complexity of the demapper is reduced with the use of simplified algorithm for 16-QAM demapping. In the later part of the paper, we consider the transmission of data over additive white class A noise (AWAN channel, using turbo coded QPSK and 16-QAM systems. We propose a novel turbo decoding scheme for AWAN channel. Also we compare the performance of turbo coded systems with QPSK and 16-QAM on AWAN channel with two different channel values- one computed as per additive white Gaussian noise (AWGN channel conditions and the other as per AWAN channel conditions. The results show that the use of appropriate channel value in turbo decoding helps to combat the impulsive noise more effectively. The proposed model for AWAN channel exhibits comparable Bit error rate (BER performance as compared to AWGN channel.
Photonic circuits for iterative decoding of a class of low-density parity-check codes
International Nuclear Information System (INIS)
Pavlichin, Dmitri S; Mabuchi, Hideo
2014-01-01
Photonic circuits in which stateful components are coupled via guided electromagnetic fields are natural candidates for resource-efficient implementation of iterative stochastic algorithms based on propagation of information around a graph. Conversely, such message=passing algorithms suggest novel circuit architectures for signal processing and computation that are well matched to nanophotonic device physics. Here, we construct and analyze a quantum optical model of a photonic circuit for iterative decoding of a class of low-density parity-check (LDPC) codes called expander codes. Our circuit can be understood as an open quantum system whose autonomous dynamics map straightforwardly onto the subroutines of an LDPC decoding scheme, with several attractive features: it can operate in the ultra-low power regime of photonics in which quantum fluctuations become significant, it is robust to noise and component imperfections, it achieves comparable performance to known iterative algorithms for this class of codes, and it provides an instructive example of how nanophotonic cavity quantum electrodynamic components can enable useful new information technology even if the solid-state qubits on which they are based are heavily dephased and cannot support large-scale entanglement. (paper)
Energy Technology Data Exchange (ETDEWEB)
Rouyer, A. [CEA Bruyeres-le-Chatel, 91 (France)
2005-10-15
Coded aperture imagery is particularly suited for imaging objects emitting penetrating radiation (hard X rays, gamma, neutrons), or for particles with rectilinear trajectories (electrons, protons, alpha particles, etc.). It is used when methods based on classical optical principles (reflection, refraction, diffraction), are invalid, or when the source emission is too weak for the well known pinhole method to give a usable image. The optical system consists in an aperture through an absorbing screen, named coding aperture, whose transmission is calculated in such a way that the spatial resolution is similar to that of a simple pinhole device, but with a far superior radiation collecting efficiency. We present a new decoding method,, called filtered autocorrelation, and illustrate its performances on images obtained with various coding apertures. (author)
Comparisons of coded aperture imaging using various apertures and decoding methods
International Nuclear Information System (INIS)
Chang, L.T.; Macdonald, B.; Perez-Mendez, V.
1976-07-01
The utility of coded aperture γ camera imaging of radioisotope distributions in Nuclear Medicine is in its ability to give depth information about a three dimensional source. We have calculated imaging with Fresnel zone plate and multiple pinhole apertures to produce coded shadows and reconstruction of these shadows using correlation, Fresnel diffraction, and Fourier transform deconvolution. Comparisons of the coded apertures and decoding methods are made by evaluating their point response functions both for in-focus and out-of-focus image planes. Background averages and standard deviations were calculated. In some cases, background subtraction was made using combinations of two complementary apertures. Results using deconvolution reconstruction for finite numbers of events are also given
Weighted-Bit-Flipping-Based Sequential Scheduling Decoding Algorithms for LDPC Codes
Directory of Open Access Journals (Sweden)
Qing Zhu
2013-01-01
Full Text Available Low-density parity-check (LDPC codes can be applied in a lot of different scenarios such as video broadcasting and satellite communications. LDPC codes are commonly decoded by an iterative algorithm called belief propagation (BP over the corresponding Tanner graph. The original BP updates all the variable-nodes simultaneously, followed by all the check-nodes simultaneously as well. We propose a sequential scheduling algorithm based on weighted bit-flipping (WBF algorithm for the sake of improving the convergence speed. Notoriously, WBF is a low-complexity and simple algorithm. We combine it with BP to obtain advantages of these two algorithms. Flipping function used in WBF is borrowed to determine the priority of scheduling. Simulation results show that it can provide a good tradeoff between FER performance and computation complexity for short-length LDPC codes.
Du, Jing; Wang, Jian
2015-11-01
Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.
Belief propagation decoding of quantum channels by passing quantum messages
International Nuclear Information System (INIS)
Renes, Joseph M
2017-01-01
The belief propagation (BP) algorithm is a powerful tool in a wide range of disciplines from statistical physics to machine learning to computational biology, and is ubiquitous in decoding classical error-correcting codes. The algorithm works by passing messages between nodes of the factor graph associated with the code and enables efficient decoding of the channel, in some cases even up to the Shannon capacity. Here we construct the first BP algorithm which passes quantum messages on the factor graph and is capable of decoding the classical–quantum channel with pure state outputs. This gives explicit decoding circuits whose number of gates is quadratic in the code length. We also show that this decoder can be modified to work with polar codes for the pure state channel and as part of a decoder for transmitting quantum information over the amplitude damping channel. These represent the first explicit capacity-achieving decoders for non-Pauli channels. (fast track communication)
Belief propagation decoding of quantum channels by passing quantum messages
Renes, Joseph M.
2017-07-01
The belief propagation (BP) algorithm is a powerful tool in a wide range of disciplines from statistical physics to machine learning to computational biology, and is ubiquitous in decoding classical error-correcting codes. The algorithm works by passing messages between nodes of the factor graph associated with the code and enables efficient decoding of the channel, in some cases even up to the Shannon capacity. Here we construct the first BP algorithm which passes quantum messages on the factor graph and is capable of decoding the classical-quantum channel with pure state outputs. This gives explicit decoding circuits whose number of gates is quadratic in the code length. We also show that this decoder can be modified to work with polar codes for the pure state channel and as part of a decoder for transmitting quantum information over the amplitude damping channel. These represent the first explicit capacity-achieving decoders for non-Pauli channels.
International Nuclear Information System (INIS)
Hasegawa, Takeo; Hashiba, Hiroshi; Akagi, Kiyoshi; Kobayashi, Akitoshi; Matsuda, Magoichi
1979-01-01
Research has been done on optically reconstructed imaging employing the Multiple Pinhole Coded Aperture (hereafter abbreviated as MPCA) in radioisotope tomographic imaging. However, problems remain in the optically reconstructed image method. Therefore, we employed a minicomputer (hereafter abbreviated as CPU) and developed the software for decoding and managing the radioisotope tomographic image. Combining the MPCA and the CPU system, we were able to decode and manage the radioisotope tomographic image. 1) In comparison to the optically decoded MPCA image, various input commands are possibly in the CPU method according to the dialogue between the CPU and the on line typewriter. In addition to this, decoded tomographic images of unrestricted depth are readily attainable. 2) In the CPU method noise elimination and other aspects of image management can be easily performed. (author)
Key-equations for list decoding of Reed-Solomon codes and how to solve them
DEFF Research Database (Denmark)
Beelen, Peter; Brander, Kristian
2010-01-01
A Reed-Solomon code of length n can be list decoded using the well-known Guruswami-Sudan algorithm. By a result of Alekhnovich (2005) the interpolation part in this algorithm can be done in complexity O(s^4l^4nlog^2nloglogn), where l denotes the designed list size and s the multiplicity parameter....... The parameters l and s are sometimes considered to be constants in the complexity analysis, but for high rate Reed-Solomon codes, their values can be very large. In this paper we will combine ideas from Alekhnovich (2005) and the concept of key equations to get an algorithm that has complexity O(sl^4nlog^2...
International Nuclear Information System (INIS)
Huang Hai-Ping
2015-01-01
The statistical physics properties of low-density parity-check codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check (bit) nodes have higher decoding thresholds compared to regular counterparts with homogeneous degree distribution. We also show that the instability of the mean-field calculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed (searching for the ground state), we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is close to the dynamical transition where all local search heuristics fail to identify the true message (codeword or the ferromagnetic state). After the dynamical transition, the number of metastable states with larger energy density (than the ferromagnetic state) becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentially numerous codewords sharing the identical ferromagnetic energy. (condensed matter: electronic structure, electrical, magnetic, and optical properties)
Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes
Jing, Lin; Brun, Todd; Quantum Research Team
Quasi-cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Two distinct, orthogonal matrices Hc and Hd are used. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation. Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes.
Iterative decoding of SOVA and LDPC product code for bit-patterned media recoding
Jeong, Seongkwon; Lee, Jaejin
2018-05-01
The demand for high-density storage systems has increased due to the exponential growth of data. Bit-patterned media recording (BPMR) is one of the promising technologies to achieve the density of 1Tbit/in2 and higher. To increase the areal density in BPMR, the spacing between islands needs to be reduced, yet this aggravates inter-symbol interference and inter-track interference and degrades the bit error rate performance. In this paper, we propose a decision feedback scheme using low-density parity check (LDPC) product code for BPMR. This scheme can improve the decoding performance using an iterative approach with extrinsic information and log-likelihood ratio value between iterative soft output Viterbi algorithm and LDPC product code. Simulation results show that the proposed LDPC product code can offer 1.8dB and 2.3dB gains over the one LDPC code at the density of 2.5 and 3 Tb/in2, respectively, when bit error rate is 10-6.
Zydziak, Nicolas; Konrad, Waldemar; Feist, Florian; Afonin, Sergii; Weidner, Steffen; Barner-Kowollik, Christopher
2016-11-30
Designing artificial macromolecules with absolute sequence order represents a considerable challenge. Here we report an advanced light-induced avenue to monodisperse sequence-defined functional linear macromolecules up to decamers via a unique photochemical approach. The versatility of the synthetic strategy-combining sequential and modular concepts-enables the synthesis of perfect macromolecules varying in chemical constitution and topology. Specific functions are placed at arbitrary positions along the chain via the successive addition of monomer units and blocks, leading to a library of functional homopolymers, alternating copolymers and block copolymers. The in-depth characterization of each sequence-defined chain confirms the precision nature of the macromolecules. Decoding of the functional information contained in the molecular structure is achieved via tandem mass spectrometry without recourse to their synthetic history, showing that the sequence information can be read. We submit that the presented photochemical strategy is a viable and advanced concept for coding individual monomer units along a macromolecular chain.
Coding/decoding and reversibility of droplet trains in microfluidic networks.
Fuerstman, Michael J; Garstecki, Piotr; Whitesides, George M
2007-02-09
Droplets of one liquid suspended in a second, immiscible liquid move through a microfluidic device in which a channel splits into two branches that reconnect downstream. The droplets choose a path based on the number of droplets that occupy each branch. The interaction among droplets in the channels results in complex sequences of path selection. The linearity of the flow through the microchannels, however, ensures that the behavior of the system can be reversed. This reversibility makes it possible to encrypt and decrypt signals coded in the intervals between droplets. The encoding/decoding device is a functional microfluidic system that requires droplets to navigate a network in a precise manner without the use of valves, switches, or other means of external control.
Gallager error-correcting codes for binary asymmetric channels
International Nuclear Information System (INIS)
Neri, I; Skantzos, N S; Bollé, D
2008-01-01
We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characterizing solutions of recursive equations of distributions for cavity fields
Fast Erasure-and error decoding of algebraic geometry codes up to the Feng-Rao bound
DEFF Research Database (Denmark)
Høholdt, Tom; Jensen, Helge Elbrønd; Sakata, Shojiro
1998-01-01
This correspondence gives an errata (that is erasure-and error-) decoding algorithm of one-point algebraic-geometry codes up to the Feng-Rao designed minimum distance using Sakata's multidimensional generalization of the Berlekamp-Massey algorithm and the voting procedure of Feng and Rao....
Hard decoding algorithm for optimizing thresholds under general Markovian noise
Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond
2017-04-01
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.
Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang
2017-09-06
The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.
Instantly decodable network coding for real-time device-to-device communications
Douik, Ahmed
2016-01-04
This paper studies the delay reduction problem for instantly decodable network coding (IDNC)-based device-to-device (D2D) communication-enabled networks. Unlike conventional point-to-multipoint (PMP) systems in which the wireless base station has the sufficient computation abilities, D2D networks rely on battery-powered operations of the devices. Therefore, a particular emphasis on the computation complexity needs to be addressed in the design of delay reduction algorithms for D2D networks. While most of the existing literature on IDNC directly extend the delay reduction PMP schemes, known to be NP-hard, to the D2D setting, this paper proposes to investigate and minimize the complexity of such algorithms for battery-powered devices. With delay minimization problems in IDNC-based systems being equivalent to a maximum weight clique problems in the IDNC graph, the presented algorithms, in this paper, can be applied to different delay aspects. This paper introduces and focuses on the reduction of the maximum value of the decoding delay as it represents the most general solution. The complexity of the solution is reduced by first proposing efficient methods for the construction, the update, and the dimension reduction of the IDNC graph. The paper, further, shows that, under particular scenarios, the problem boils down to a maximum clique problem. Due to the complexity of discovering such maximum clique, the paper presents a fast selection algorithm. Simulation results illustrate the performance of the proposed schemes and suggest that the proposed fast selection algorithm provides appreciable complexity gain as compared to the optimal selection one, with a negligible degradation in performance. In addition, they indicate that the running time of the proposed solution is close to the random selection algorithm.
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom; Hjaltason, Johan
2005-01-01
We analyze the relation between iterative decoding and the extended parity check matrix. By considering a modified version of bit flipping, which produces a list of decoded words, we derive several relations between decodable error patterns and the parameters of the code. By developing a tree...... of codewords at minimal distance from the received vector, we also obtain new information about the code....
Coding/decoding two-dimensional images with orbital angular momentum of light.
Chu, Jiaqi; Li, Xuefeng; Smithwick, Quinn; Chu, Daping
2016-04-01
We investigate encoding and decoding of two-dimensional information using the orbital angular momentum (OAM) of light. Spiral phase plates and phase-only spatial light modulators are used in encoding and decoding of OAM states, respectively. We show that off-axis points and spatial variables encoded with a given OAM state can be recovered through decoding with the corresponding complimentary OAM state.
A Low-Complexity Joint Detection-Decoding Algorithm for Nonbinary LDPC-Coded Modulation Systems
Wang, Xuepeng; Bai, Baoming; Ma, Xiao
2010-01-01
In this paper, we present a low-complexity joint detection-decoding algorithm for nonbinary LDPC codedmodulation systems. The algorithm combines hard-decision decoding using the message-passing strategy with the signal detector in an iterative manner. It requires low computational complexity, offers good system performance and has a fast rate of decoding convergence. Compared to the q-ary sum-product algorithm (QSPA), it provides an attractive candidate for practical applications of q-ary LDP...
Tensor Networks and Quantum Error Correction
Ferris, Andrew J.; Poulin, David
2014-07-01
We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.
Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes
Harrington, James William
Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present
The Three Stages of Coding and Decoding in Listening Courses of College Japanese Specialty
Yang, Fang
2008-01-01
The main focus of research papers on listening teaching published in recent years is the theoretical meanings of decoding on the training of listening comprehension ability. Although in many research papers the bottom-up approach and top-down approach, information processing mode theory, are applied to illustrate decoding and to emphasize the…
A lossy graph model for delay reduction in generalized instantly decodable network coding
Douik, Ahmed S.; Sorour, Sameh; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2014-01-01
, arising from lossy feedback events, when the expected decoding delay of XORing them among themselves or with other certain packets is lower than that expected when sending these packets separately. We compare the decoding delay performance of LG-IDNC and G
Decoding the non-coding genome: elucidating genetic risk outside the coding genome.
Barr, C L; Misener, V L
2016-01-01
Current evidence emerging from genome-wide association studies indicates that the genetic underpinnings of complex traits are likely attributable to genetic variation that changes gene expression, rather than (or in combination with) variation that changes protein-coding sequences. This is particularly compelling with respect to psychiatric disorders, as genetic changes in regulatory regions may result in differential transcriptional responses to developmental cues and environmental/psychosocial stressors. Until recently, however, the link between transcriptional regulation and psychiatric genetic risk has been understudied. Multiple obstacles have contributed to the paucity of research in this area, including challenges in identifying the positions of remote (distal from the promoter) regulatory elements (e.g. enhancers) and their target genes and the underrepresentation of neural cell types and brain tissues in epigenome projects - the availability of high-quality brain tissues for epigenetic and transcriptome profiling, particularly for the adolescent and developing brain, has been limited. Further challenges have arisen in the prediction and testing of the functional impact of DNA variation with respect to multiple aspects of transcriptional control, including regulatory-element interaction (e.g. between enhancers and promoters), transcription factor binding and DNA methylation. Further, the brain has uncommon DNA-methylation marks with unique genomic distributions not found in other tissues - current evidence suggests the involvement of non-CG methylation and 5-hydroxymethylation in neurodevelopmental processes but much remains unknown. We review here knowledge gaps as well as both technological and resource obstacles that will need to be overcome in order to elucidate the involvement of brain-relevant gene-regulatory variants in genetic risk for psychiatric disorders. © 2015 John Wiley & Sons Ltd and International Behavioural and Neural Genetics Society.
Joint Decoding of Concatenated VLEC and STTC System
Directory of Open Access Journals (Sweden)
Chen Huijun
2008-01-01
Full Text Available Abstract We consider the decoding of wireless communication systems with both source coding in the application layer and channel coding in the physical layer for high-performance transmission over fading channels. Variable length error correcting codes (VLECs and space time trellis codes (STTCs are used to provide bandwidth efficient data compression as well as coding and diversity gains. At the receiver, an iterative joint source and space time decoding scheme are developed to utilize redundancy in both STTC and VLEC to improve overall decoding performance. Issues such as the inseparable systematic information in the symbol level, the asymmetric trellis structure of VLEC, and information exchange between bit and symbol domains have been considered in the maximum a posteriori probability (MAP decoding algorithm. Simulation results indicate that the developed joint decoding scheme achieves a significant decoding gain over the separate decoding in fading channels, whether or not the channel information is perfectly known at the receiver. Furthermore, how rate allocation between STTC and VLEC affects the performance of the joint source and space-time decoder is investigated. Different systems with a fixed overall information rate are studied. It is shown that for a system with more redundancy dedicated to the source code and a higher order modulation of STTC, the joint decoding yields better performance, though with increased complexity.
Joint Decoding of Concatenated VLEC and STTC System
Directory of Open Access Journals (Sweden)
Huijun Chen
2008-07-01
Full Text Available We consider the decoding of wireless communication systems with both source coding in the application layer and channel coding in the physical layer for high-performance transmission over fading channels. Variable length error correcting codes (VLECs and space time trellis codes (STTCs are used to provide bandwidth efficient data compression as well as coding and diversity gains. At the receiver, an iterative joint source and space time decoding scheme are developed to utilize redundancy in both STTC and VLEC to improve overall decoding performance. Issues such as the inseparable systematic information in the symbol level, the asymmetric trellis structure of VLEC, and information exchange between bit and symbol domains have been considered in the maximum a posteriori probability (MAP decoding algorithm. Simulation results indicate that the developed joint decoding scheme achieves a significant decoding gain over the separate decoding in fading channels, whether or not the channel information is perfectly known at the receiver. Furthermore, how rate allocation between STTC and VLEC affects the performance of the joint source and space-time decoder is investigated. Different systems with a fixed overall information rate are studied. It is shown that for a system with more redundancy dedicated to the source code and a higher order modulation of STTC, the joint decoding yields better performance, though with increased complexity.
A class of burst-correcting array codes
Blaum, M.; Farrell, P.G.; Tilborg, van H.C.A.
1986-01-01
The usual (k_{2} + 1) times (k_{1} + 1) array code, in which the last row and the last column contain redundant bits, can correct any single error. However, if the bits are read diagonally instead of horizontally, the code can correct bursts of errors. It is shown that the(_{k}2 + 1) times (k_{1} +
Huang, Jen-Fa; Yang, Chao-Chin; Tseng, Shin-Pin
2004-01-01
In this paper, an optical code-division multiple-access (OCDMA) system with complementary Walsh-Hadamard coded optical encoder/decoder configuration structured over arrayed-waveguide grating (AWG) routers is examined. In the proposed system, each network user requires only two AWG routers to accomplish spectral encoding and decoding for complementary keying, thus, resulting a simpler and low cost system. Performance of the proposed system is analyzed by taking the effect of phase-induced intensity noise into account. The result indicates that the established system not only preserves the capability of suppressing multiple-access interference (MAI), but also improves bit-error-rate performance as compared to the conventional coders employing simple on-off keying.
Fast Maximum-Likelihood Decoder for Quasi-Orthogonal Space-Time Block Code
Directory of Open Access Journals (Sweden)
Adel Ahmadi
2015-01-01
Full Text Available Motivated by the decompositions of sphere and QR-based methods, in this paper we present an extremely fast maximum-likelihood (ML detection approach for quasi-orthogonal space-time block code (QOSTBC. The proposed algorithm with a relatively simple design exploits structure of quadrature amplitude modulation (QAM constellations to achieve its goal and can be extended to any arbitrary constellation. Our decoder utilizes a new decomposition technique for ML metric which divides the metric into independent positive parts and a positive interference part. Search spaces of symbols are substantially reduced by employing the independent parts and statistics of noise. Symbols within the search spaces are successively evaluated until the metric is minimized. Simulation results confirm that the proposed decoder’s performance is superior to many of the recently published state-of-the-art solutions in terms of complexity level. More specifically, it was possible to verify that application of the new algorithms with 1024-QAM would decrease the computational complexity compared to state-of-the-art solution with 16-QAM.
Han, Yishi; Luo, Zhixiao; Wang, Jianhua; Min, Zhixuan; Qin, Xinyu; Sun, Yunlong
2014-09-01
In general, context-based adaptive variable length coding (CAVLC) decoding in H.264/AVC standard requires frequent access to the unstructured variable length coding tables (VLCTs) and significant memory accesses are consumed. Heavy memory accesses will cause high power consumption and time delays, which are serious problems for applications in portable multimedia devices. We propose a method for high-efficiency CAVLC decoding by using a program instead of all the VLCTs. The decoded codeword from VLCTs can be obtained without any table look-up and memory access. The experimental results show that the proposed algorithm achieves 100% memory access saving and 40% decoding time saving without degrading video quality. Additionally, the proposed algorithm shows a better performance compared with conventional CAVLC decoding, such as table look-up by sequential search, table look-up by binary search, Moon's method, and Kim's method.
Resource Efficient LDPC Decoders for Multimedia Communication
Chandrasetty, Vikram Arkalgud; Aziz, Syed Mahfuzul
2013-01-01
Achieving high image quality is an important aspect in an increasing number of wireless multimedia applications. These applications require resource efficient error correction hardware to detect and correct errors introduced by the communication channel. This paper presents an innovative flexible architecture for error correction using Low-Density Parity-Check (LDPC) codes. The proposed partially-parallel decoder architecture utilizes a novel code construction technique based on multi-level H...
Image transmission system using adaptive joint source and channel decoding
Liu, Weiliang; Daut, David G.
2005-03-01
In this paper, an adaptive joint source and channel decoding method is designed to accelerate the convergence of the iterative log-dimain sum-product decoding procedure of LDPC codes as well as to improve the reconstructed image quality. Error resilience modes are used in the JPEG2000 source codec, which makes it possible to provide useful source decoded information to the channel decoder. After each iteration, a tentative decoding is made and the channel decoded bits are then sent to the JPEG2000 decoder. Due to the error resilience modes, some bits are known to be either correct or in error. The positions of these bits are then fed back to the channel decoder. The log-likelihood ratios (LLR) of these bits are then modified by a weighting factor for the next iteration. By observing the statistics of the decoding procedure, the weighting factor is designed as a function of the channel condition. That is, for lower channel SNR, a larger factor is assigned, and vice versa. Results show that the proposed joint decoding methods can greatly reduce the number of iterations, and thereby reduce the decoding delay considerably. At the same time, this method always outperforms the non-source controlled decoding method up to 5dB in terms of PSNR for various reconstructed images.
Optimal coding-decoding for systems controlled via a communication channel
Yi-wei, Feng; Guo, Ge
2013-12-01
In this article, we study the problem of controlling plants over a signal-to-noise ratio (SNR) constrained communication channel. Different from previous research, this article emphasises the importance of the actual channel model and coder/decoder in the study of network performance. Our major objectives include coder/decoder design for an additive white Gaussian noise (AWGN) channel with both standard network configuration and Youla parameter network architecture. We find that the optimal coder and decoder can be realised for different network configuration. The results are useful in determining the minimum channel capacity needed in order to stabilise plants over communication channels. The coder/decoder obtained can be used to analyse the effect of uncertainty on the channel capacity. An illustrative example is provided to show the effectiveness of the results.
VLSI architectures for modern error-correcting codes
Zhang, Xinmiao
2015-01-01
Error-correcting codes are ubiquitous. They are adopted in almost every modern digital communication and storage system, such as wireless communications, optical communications, Flash memories, computer hard drives, sensor networks, and deep-space probing. New-generation and emerging applications demand codes with better error-correcting capability. On the other hand, the design and implementation of those high-gain error-correcting codes pose many challenges. They usually involve complex mathematical computations, and mapping them directly to hardware often leads to very high complexity. VLSI
A study of the decoding of multiple pinhole coded aperture RI tomographic images
International Nuclear Information System (INIS)
Hasegawa, Takeo; Kobayashi, Akitoshi; Nishiyama, Yutaka; Akagi, Kiyoshi; Uehata, Hiroshi
1981-01-01
In order to obtain a radioisotope (RI) tomographic image, there are various, methods, including the RCT method, Time Modulate method, and Multiple Pinhole Coded Aperture (MPCA) method and others. The MPCA method has several advantages. Using the MPCA method, there is no need to move either the detector or the patient, Furthermore, the generally used γ-camera may be used without any alterations. Due to certain problems in reconstructing the tomographic image, the use of the MPCA method in clinical practice is limited to representation of small organs (e.g. heart) using the 7-Pinhole collimator. This research presents an experimental approach to overcome the problems in reconstruction of tomographic images of large organs (organs other than the heart, such as the brain, liver, lung etc.) by introducing a reconstruction algorithm and correction software into the MPCA method. There are 2 main problems in MPCA image reconstruction: (1) Due to the rounding-off procedure, there is both point omission and shifting of point coordinates. (2) The central portion is characterized by high-counts. Both of these problems were solved by incorporating a reconstruction algorithm and a correction function. The resultant corrected tomographic image was processed using a filter derived from subjecting a PSF to a Fourier transform. Thus, it has become possible to obtain a high-quality tomographic image of large organs for clinical use. (author)
Video coding and decoding devices and methods preserving PPG relevant information
2015-01-01
The present invention relates to a video encoding device (10, 10', 10") and method for encoding video data and to a corresponding video decoding device (60, 60') and method. To preserve PPG relevant information after encoding without requiring a large amount of additional data for the video encoder
Video coding and decoding devices and methods preserving ppg relevant information
2013-01-01
The present invention relates to a video encoding device (10, 10', 10'') and method for encoding video data and to a corresponding video decoding device (60, 60') and method. To preserve PPG relevant information after encoding without requiring a large amount of additional data for the video encoder
Massey, J. L.
1976-01-01
Virtually all previously-suggested rate 1/2 binary convolutional codes with KE = 24 are compared. Their distance properties are given; and their performance, both in computation and in error probability, with sequential decoding on the deep-space channel is determined by simulation. Recommendations are made both for the choice of a specific KE = 24 code as well as for codes to be included in future coding standards for the deep-space channel. A new result given in this report is a method for determining the statistical significance of error probability data when the error probability is so small that it is not feasible to perform enough decoding simulations to obtain more than a very small number of decoding errors.
1989-01-01
Television system in which digitalized picture signals subjected to a transform coding are transmitted from an encoding station to a decoding station. In a television system a digital picture signal is subjected to a transform coding for the purpose of bit rate reduction. In order to detect motion
Structuring Interactive Correctness Proofs by Formalizing Coding Idioms
Gast, Holger
2012-01-01
This paper examines a novel strategy for developing correctness proofs in interactive software verification for C programs. Rather than proceeding backwards from the generated verification conditions, we start by developing a library of the employed data structures and related coding idioms. The application of that library then leads to correctness proofs that reflect informal arguments about the idioms. We apply this strategy to the low-level memory allocator of the L4 microkernel, a case st...
Hardware Implementation of A Non-RLL Soft-decoding Beacon-based Visible Light Communication Receiver
Nguyen, Duc-Phuc; Le, Dinh-Dung; Tran, Thi-Hong; Huynh, Huu-Thuan; Nakashima, Yasuhiko
2018-01-01
Visible light communication (VLC)-based beacon systems, which usually transmit identification (ID) information in small-size data frames are applied widely in indoor localization applications. There is one fact that flicker of LED light should be avoid in any VLC systems. Current flicker mitigation solutions based on run-length limited (RLL) codes suffer from reduced code rates, or are limited to hard-decoding forward error correction (FEC) decoders. Recently, soft-decoding techniques of RLL-...
Directory of Open Access Journals (Sweden)
TRIFINA, L.
2011-02-01
Full Text Available This paper analyzes the extrinsic information scaling coefficient influence on double-iterative decoding algorithm for space-time turbo codes with large number of antennas. The max-log-APP algorithm is used, scaling both the extrinsic information in the turbo decoder and the one used at the input of the interference-canceling block. Scaling coefficients of 0.7 or 0.75 lead to a 0.5 dB coding gain compared to the no-scaling case, for one or more iterations to cancel the spatial interferences.
Energy Efficient Error-Correcting Coding for Wireless Systems
Shao, X.
2010-01-01
The wireless channel is a hostile environment. The transmitted signal does not only suffers multi-path fading but also noise and interference from other users of the wireless channel. That causes unreliable communications. To achieve high-quality communications, error correcting coding is required
Xiong, Chenrong; Yan, Zhiyuan
2014-10-01
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for non-binary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and hence have significantly lower complexity than other algorithms. In this paper, we propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the existing majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a re-selection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, re-selecting intermediate hard decisions, and changing reliability information.
Ancheta, T. C., Jr.
1976-01-01
A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A 'universal' generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Two examples are given, comparing the performance of noiseless universal syndrome-source-coding to (1) run-length coding and (2) Lynch-Davisson-Schalkwijk-Cover universal coding for an ensemble of binary memoryless sources.
The research on multi-projection correction based on color coding grid array
Yang, Fan; Han, Cheng; Bai, Baoxing; Zhang, Chao; Zhao, Yunxiu
2017-10-01
There are many disadvantages such as lower timeliness, greater manual intervention in multi-channel projection system, in order to solve the above problems, this paper proposes a multi-projector correction technology based on color coding grid array. Firstly, a color structured light stripe is generated by using the De Bruijn sequences, then meshing the feature information of the color structured light stripe image. We put the meshing colored grid intersection as the center of the circle, and build a white solid circle as the feature sample set of projected images. It makes the constructed feature sample set not only has the perceptual localization, but also has good noise immunity. Secondly, we establish the subpixel geometric mapping relationship between the projection screen and the individual projectors by using the structure of light encoding and decoding based on the color array, and the geometrical mapping relation is used to solve the homography matrix of each projector. Lastly the brightness inconsistency of the multi-channel projection overlap area is seriously interfered, it leads to the corrected image doesn't fit well with the observer's visual needs, and we obtain the projection display image of visual consistency by using the luminance fusion correction algorithm. The experimental results show that this method not only effectively solved the problem of distortion of multi-projection screen and the issue of luminance interference in overlapping region, but also improved the calibration efficient of multi-channel projective system and reduced the maintenance cost of intelligent multi-projection system.
Symbol synchronization for the TDRSS decoder
Costello, D. J., Jr.
1983-01-01
Each 8 bits out of the Viterbi decoder correspond to one symbol of the R/S code. Synchronization must be maintained here so that each 8-bit symbol delivered to the R/S decoder corresponds to an 8-bit symbol from the R/S encoder. Lack of synchronization, would cause an error in almost every R/S symbol since even a - 1-bit sync slip shifts every bit in each 8-bit symbol by one position, therby confusing the mapping betweeen 8-bit sequences and symbols. The error correcting capability of the R/S code would be exceeded. Possible ways to correcting this condition include: (1) designing the R/S decoder to recognize the overload and shifting the output sequence of the inner decoder to establish a different sync state; (2) using the characteristics of the inner decoder to establish symbol synchronization for the outer code, with or without a deinterleaver and an interleaver; and (3) modifying the encoder to alternate periodically between two sets of generators.
Modified Decoding Algorithm of LLR-SPA
Directory of Open Access Journals (Sweden)
Zhongxun Wang
2014-09-01
Full Text Available In wireless sensor networks, the energy consumption is mainly occurred in the stage of information transmission. The Low Density Parity Check code can make full use of the channel information to save energy. Because of the widely used decoding algorithm of the Low Density Parity Check code, this paper proposes a new decoding algorithm which is based on the LLR-SPA (Sum-Product Algorithm in Log-Likelihood-domain to improve the accuracy of the decoding algorithm. In the modified algorithm, a piecewise linear function is used to approximate the complicated Jacobi correction term in LLR-SPA decoding algorithm. Construct the tangent by the tangency point to the function of Jacobi correction term, which is based on the first order Taylor Series. In this way, the proposed piecewise linear approximation offers almost a perfect match to the function of Jacobi correction term. Meanwhile, the proposed piecewise linear approximation could avoid the operation of logarithmic which is more suitable for practical application. The simulation results show that the proposed algorithm could improve the decoding accuracy greatly without noticeable variation of the computational complexity.
Matsui, Chihiro; Kinoshita, Reika; Takeuchi, Ken
2018-04-01
A hybrid of storage class memory (SCM) and NAND flash is a promising technology for high performance storage. Error correction is inevitable on SCM and NAND flash because their bit error rate (BER) increases with write/erase (W/E) cycles, data retention, and program/read disturb. In addition, scaling and multi-level cell technologies increase BER. However, error-correcting code (ECC) degrades storage performance because of extra memory reading and encoding/decoding time. Therefore, applicable ECC strength of SCM and NAND flash is evaluated independently by fixing ECC strength of one memory in the hybrid storage. As a result, weak BCH ECC with small correctable bit is recommended for the hybrid storage with large SCM capacity because SCM is accessed frequently. In contrast, strong and long-latency LDPC ECC can be applied to NAND flash in the hybrid storage with large SCM capacity because large-capacity SCM improves the storage performance.
Kong, Gyuyeol; Choi, Sooyong
2017-09-01
An enhanced 2/3 four-ary modulation code using soft-decision Viterbi decoding is proposed for four-level holographic data storage systems. While the previous four-ary modulation codes focus on preventing maximum two-dimensional intersymbol interference patterns, the proposed four-ary modulation code aims at maximizing the coding gains for better bit error rate performances. For achieving significant coding gains from the four-ary modulation codes, we design a new 2/3 four-ary modulation code in order to enlarge the free distance on the trellis through extensive simulation. The free distance of the proposed four-ary modulation code is extended from 1.21 to 2.04 compared with that of the conventional four-ary modulation code. The simulation result shows that the proposed four-ary modulation code has more than 1 dB gains compared with the conventional four-ary modulation code.
Quantum quasi-cyclic low-density parity-check error-correcting codes
International Nuclear Information System (INIS)
Yuan, Li; Gui-Hua, Zeng; Lee, Moon Ho
2009-01-01
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated. (general)
Forced Sequence Sequential Decoding
DEFF Research Database (Denmark)
Jensen, Ole Riis
In this thesis we describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon codes with non-uniform profile. With this scheme decoding with good performance...... is possible as low as Eb/No=0.6 dB, which is about 1.7 dB below the signal-to-noise ratio that marks the cut-off rate for the convolutional code. This is possible since the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability...... of computational overflow. Analytical results for the probability that the first Reed-Solomon word is decoded after C computations are presented. This is supported by simulation results that are also extended to other parameters....
Binary Linear-Time Erasure Decoding for Non-Binary LDPC codes
Savin, Valentin
2009-01-01
In this paper, we first introduce the extended binary representation of non-binary codes, which corresponds to a covering graph of the bipartite graph associated with the non-binary code. Then we show that non-binary codewords correspond to binary codewords of the extended representation that further satisfy some simplex-constraint: that is, bits lying over the same symbol-node of the non-binary graph must form a codeword of a simplex code. Applied to the binary erasure channel, this descript...
Optimal quantum error correcting codes from absolutely maximally entangled states
Raissi, Zahra; Gogolin, Christian; Riera, Arnau; Acín, Antonio
2018-02-01
Absolutely maximally entangled (AME) states are pure multi-partite generalizations of the bipartite maximally entangled states with the property that all reduced states of at most half the system size are in the maximally mixed state. AME states are of interest for multipartite teleportation and quantum secret sharing and have recently found new applications in the context of high-energy physics in toy models realizing the AdS/CFT-correspondence. We work out in detail the connection between AME states of minimal support and classical maximum distance separable (MDS) error correcting codes and, in particular, provide explicit closed form expressions for AME states of n parties with local dimension \
Quantum secret sharing based on quantum error-correcting codes
International Nuclear Information System (INIS)
Zhang Zu-Rong; Liu Wei-Tao; Li Cheng-Zu
2011-01-01
Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k − 1, 1, k] quantum error-correcting code (QECC) to implement a quantum (k, 2k − 1) threshold scheme. It also takes advantage of classical enhancement of the [2k − 1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels. (general)
Discussion on LDPC Codes and Uplink Coding
Andrews, Ken; Divsalar, Dariush; Dolinar, Sam; Moision, Bruce; Hamkins, Jon; Pollara, Fabrizio
2007-01-01
This slide presentation reviews the progress that the workgroup on Low-Density Parity-Check (LDPC) for space link coding. The workgroup is tasked with developing and recommending new error correcting codes for near-Earth, Lunar, and deep space applications. Included in the presentation is a summary of the technical progress of the workgroup. Charts that show the LDPC decoder sensitivity to symbol scaling errors are reviewed, as well as a chart showing the performance of several frame synchronizer algorithms compared to that of some good codes and LDPC decoder tests at ESTL. Also reviewed is a study on Coding, Modulation, and Link Protocol (CMLP), and the recommended codes. A design for the Pseudo-Randomizer with LDPC Decoder and CRC is also reviewed. A chart that summarizes the three proposed coding systems is also presented.
The Irony of Ethics: (De)coding the Lived Experience of Women and Minority Faculty
Reybold, L. Earle
2014-01-01
What does it mean to "be" an ethical faculty member? A number of scholars point to legal and moral issues, aligning ethics with professional codes and regulated by institutional policy. From this perspective, being ethical is a matter of knowing and following the professional rules--the goal is to avoid certain actions. On the other…
Control of Fur synthesis by the non-coding RNA RyhB and iron-responsive decoding.
Vecerek, Branislav; Moll, Isabella; Bläsi, Udo
2007-02-21
The Fe2+-dependent Fur protein serves as a negative regulator of iron uptake in bacteria. As only metallo-Fur acts as an autogeneous repressor, Fe2+scarcity would direct fur expression when continued supply is not obviously required. We show that in Escherichia coli post-transcriptional regulatory mechanisms ensure that Fur synthesis remains steady in iron limitation. Our studies revealed that fur translation is coupled to that of an upstream open reading frame (uof), translation of which is downregulated by the non-coding RNA (ncRNA) RyhB. As RyhB transcription is negatively controlled by metallo-Fur, iron depletion creates a negative feedback loop. RyhB-mediated regulation of uof-fur provides the first example for indirect translational regulation by a trans-encoded ncRNA. In addition, we present evidence for an iron-responsive decoding mechanism of the uof-fur entity. It could serve as a backup mechanism of the RyhB circuitry, and represents the first link between iron availability and synthesis of an iron-containing protein.
Kirvelis, Dobilas; Beitas, Kastytis
2008-10-01
The aim of this work is to show that the essence of life and living systems is their organization as bioinformational technology on the base of informational anticipatory control. Principal paradigmatic and structural schemes of functional organization of life (organisms and their systems) are constructed on the basis of systemic analysis and synthesis of main phenomenological features of living world. Life is based on functional elements that implement engineering procedures of closed-loop coding-decoding control (CL-CDC). Phenomenon of natural bioinformational control appeared and developed on the Earth 3-4 bln years ago, when the life originated as a result of chemical and later biological evolution. Informatics paradigm considers the physical and chemical transformations of energy and matter in organized systems as flows that are controlled and the signals as means for purposive informational control programs. The social and technical technological systems as informational control systems are a latter phenomenon engineered by man. The information emerges in organized systems as a necessary component of control technology. Generalized schemes of functional organization on levels of cell, organism and brain neocortex, as the highest biosystem with CL-CDC, are presented. CL-CDC concept expands the understanding of bioinformatics.
The effectiveness of correcting codes in reception in the whole in additive normal white noise
Shtarkov, Y. M.
1974-01-01
Some possible criteria for estimating the effectiveness of correcting codes are presented, and the energy effectiveness of correcting codes is studied for symbol-by-symbol reception. Expressions for the energetic effectiveness of binary correcting codes for reception in the whole are produced. Asymptotic energetic effectiveness and finite signal/noise ratio cases are considered.
Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation
International Nuclear Information System (INIS)
Alber, G.; Mussinger, M.; Beth, Th.; Charnes, Ch.; Delgado, A.; Grassl, M.
2003-01-01
The recently introduced detected-jump-correcting quantum codes are capable of stabilizing qubit systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit classical information about which qubit has emitted spontaneously and correspond to an active error-correcting code embedded in a passive error-correcting code. The construction of a family of one-detected-jump-error-correcting quantum codes is shown and the optimal redundancy, encoding, and recovery as well as general properties of detected-jump-error-correcting quantum codes are discussed. By the use of design theory, multiple-jump-error-correcting quantum codes can be constructed. The performance of one-jump-error-correcting quantum codes under nonideal conditions is studied numerically by simulating a quantum memory and Grover's algorithm
Quantum error-correcting code for ternary logic
Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita
2018-05-01
Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.
Forced Sequence Sequential Decoding
DEFF Research Database (Denmark)
Jensen, Ole Riis; Paaske, Erik
1998-01-01
We describe a new concatenated decoding scheme based on iterations between an inner sequentially decoded convolutional code of rate R=1/4 and memory M=23, and block interleaved outer Reed-Solomon (RS) codes with nonuniform profile. With this scheme decoding with good performance is possible as low...... as Eb/N0=0.6 dB, which is about 1.25 dB below the signal-to-noise ratio (SNR) that marks the cutoff rate for the full system. Accounting for about 0.45 dB due to the outer codes, sequential decoding takes place at about 1.7 dB below the SNR cutoff rate for the convolutional code. This is possible since...... the iteration process provides the sequential decoders with side information that allows a smaller average load and minimizes the probability of computational overflow. Analytical results for the probability that the first RS word is decoded after C computations are presented. These results are supported...
Application of Beyond Bound Decoding for High Speed Optical Communications
DEFF Research Database (Denmark)
Li, Bomin; Larsen, Knud J.; Vegas Olmos, Juan José
2013-01-01
This paper studies the application of beyond bound decoding method for high speed optical communications. This hard-decision decoding method outperforms traditional minimum distance decoding method, with a total net coding gain of 10.36 dB.......This paper studies the application of beyond bound decoding method for high speed optical communications. This hard-decision decoding method outperforms traditional minimum distance decoding method, with a total net coding gain of 10.36 dB....
Decoding the usefulness of non-coding RNAs as breast cancer markers.
Amorim, Maria; Salta, Sofia; Henrique, Rui; Jerónimo, Carmen
2016-09-15
Although important advances in the management of breast cancer (BC) have been recently accomplished, it still constitutes the leading cause of cancer death in women worldwide. BC is a heterogeneous and complex disease, making clinical prediction of outcome a very challenging task. In recent years, gene expression profiling emerged as a tool to assist in clinical decision, enabling the identification of genetic signatures that better predict prognosis and response to therapy. Nevertheless, translation to routine practice has been limited by economical and technical reasons and, thus, novel biomarkers, especially those requiring non-invasive or minimally invasive collection procedures, while retaining high sensitivity and specificity might represent a significant development in this field. An increasing amount of evidence demonstrates that non-coding RNAs (ncRNAs), particularly microRNAs (miRNAs) and long noncoding RNAs (lncRNAs), are aberrantly expressed in several cancers, including BC. miRNAs are of particular interest as new, easily accessible, cost-effective and non-invasive tools for precise management of BC patients because they circulate in bodily fluids (e.g., serum and plasma) in a very stable manner, enabling BC assessment and monitoring through liquid biopsies. This review focus on how ncRNAs have the potential to answer present clinical needs in the personalized management of patients with BC and comprehensively describes the state of the art on the role of ncRNAs in the diagnosis, prognosis and prediction of response to therapy in BC.
Decoding critical long non-coding RNA in ovarian cancer epithelial-to-mesenchymal transition.
Mitra, Ramkrishna; Chen, Xi; Greenawalt, Evan J; Maulik, Ujjwal; Jiang, Wei; Zhao, Zhongming; Eischen, Christine M
2017-11-17
Long non-coding RNA (lncRNA) are emerging as contributors to malignancies. Little is understood about the contribution of lncRNA to epithelial-to-mesenchymal transition (EMT), which correlates with metastasis. Ovarian cancer is usually diagnosed after metastasis. Here we report an integrated analysis of >700 ovarian cancer molecular profiles, including genomic data sets, from four patient cohorts identifying lncRNA DNM3OS, MEG3, and MIAT overexpression and their reproducible gene regulation in ovarian cancer EMT. Genome-wide mapping shows 73% of MEG3-regulated EMT-linked pathway genes contain MEG3 binding sites. DNM3OS overexpression, but not MEG3 or MIAT, significantly correlates to worse overall patient survival. DNM3OS knockdown results in altered EMT-linked genes/pathways, mesenchymal-to-epithelial transition, and reduced cell migration and invasion. Proteotranscriptomic characterization further supports the DNM3OS and ovarian cancer EMT connection. TWIST1 overexpression and DNM3OS amplification provides an explanation for increased DNM3OS levels. Therefore, our results elucidate lncRNA that regulate EMT and demonstrate DNM3OS specifically contributes to EMT in ovarian cancer.
De Marchi, Luca; Marzani, Alessandro; Moll, Jochen; Kudela, Paweł; Radzieński, Maciej; Ostachowicz, Wiesław
2017-07-01
The performance of Lamb wave based monitoring systems, both in terms of diagnosis time and data complexity, can be enhanced by increasing the number of transducers used to actuate simultaneously the guided waves in the inspected medium. However, in case of multiple simultaneously-operated actuators the interference among the excited wave modes within the acquired signals has to be considered for the further processing. To this aim, in this work a code division strategy based on the Warped Frequency Transform is presented. At first, the proposed procedure encodes actuation pulses using Gold sequences. Next, for each considered actuator the acquired signals are compensated from dispersion by cross correlating the warped version of the actuated and received signals. Compensated signals form the base for a final wavenumber imaging meant at emphasizing defects and or anomalies by removing incident wavefield and edge reflections. The proposed strategy is tested numerically, and validated through an experiment in which guided waves are actuated in a plate by four piezoelectric transducers operating simultaneously.
Analysis and Design of Binary Message-Passing Decoders
DEFF Research Database (Denmark)
Lechner, Gottfried; Pedersen, Troels; Kramer, Gerhard
2012-01-01
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results...... message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived....... in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary...
DEFF Research Database (Denmark)
Martinez Peñas, Umberto; Pellikaan, Ruud
2017-01-01
Error-correcting pairs were introduced as a general method of decoding linear codes with respect to the Hamming metric using coordinatewise products of vectors, and are used for many well-known families of codes. In this paper, we define new types of vector products, extending the coordinatewise ...
Correcting quantum errors with entanglement.
Brun, Todd; Devetak, Igor; Hsieh, Min-Hsiu
2006-10-20
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.
Decoding the productivity code
DEFF Research Database (Denmark)
Hansen, David
. Improvement leaders can combine different improvement approaches, here problem solving and strength-based thinking, to achieve ambidextrous improvement capability that can balance exploitation and exploration. An organizational transformation is necessary to develop continuous improvement capability...... also showed that organizational transformation is not about changing people’s thinking or training them in new methods, but rather about the development of a coherent improvement system and the competence to initiate and management improvement processes in an organizational setting. The study......This thesis introduces a new perspective on how organizations can achieve sustainable organizational performance in a changing world. By integrating Lean, the strength-based perspective, and organizational development, the false dichotomy and struggle between rationalization and employee well being...
Video encoder/decoder for encoding/decoding motion compensated images
1996-01-01
Video encoder and decoder, provided with a motion compensator for motion-compensated video coding or decoding in which a picture is coded or decoded in blocks in alternately horizontal and vertical steps. The motion compensator is provided with addressing means (160) and controlled multiplexers
Decoding communities in networks
Radicchi, Filippo
2018-02-01
According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and nonedges in the network are parity bits introduced by the encoder but degraded through the channel, and a community identification algorithm is a decoder. The interpretation is perfectly equivalent to the one at the basis of well-known statistical inference algorithms for community detection. The only difference in the interpretation is that a noisy channel replaces a stochastic network model. However, the different perspective gives the opportunity to take advantage of the rich set of tools of coding theory to generate novel insights on the problem of community detection. In this paper, we illustrate two main applications of standard coding-theoretical methods to community detection. First, we leverage a state-of-the-art decoding technique to generate a family of quasioptimal community detection algorithms. Second and more important, we show that the Shannon's noisy-channel coding theorem can be invoked to establish a lower bound, here named as decodability bound, for the maximum amount of noise tolerable by an ideal decoder to achieve perfect detection of communities. When computed for well-established synthetic benchmarks, the decodability bound explains accurately the performance achieved by the best community detection algorithms existing on the market, telling us that only little room for their improvement is still potentially left.
Decoding communities in networks.
Radicchi, Filippo
2018-02-01
According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and nonedges in the network are parity bits introduced by the encoder but degraded through the channel, and a community identification algorithm is a decoder. The interpretation is perfectly equivalent to the one at the basis of well-known statistical inference algorithms for community detection. The only difference in the interpretation is that a noisy channel replaces a stochastic network model. However, the different perspective gives the opportunity to take advantage of the rich set of tools of coding theory to generate novel insights on the problem of community detection. In this paper, we illustrate two main applications of standard coding-theoretical methods to community detection. First, we leverage a state-of-the-art decoding technique to generate a family of quasioptimal community detection algorithms. Second and more important, we show that the Shannon's noisy-channel coding theorem can be invoked to establish a lower bound, here named as decodability bound, for the maximum amount of noise tolerable by an ideal decoder to achieve perfect detection of communities. When computed for well-established synthetic benchmarks, the decodability bound explains accurately the performance achieved by the best community detection algorithms existing on the market, telling us that only little room for their improvement is still potentially left.
Coding "Corrective Recasts": The Maintenance of Meaning and More Fundamental Problems
Hauser, Eric
2005-01-01
A fair amount of descriptive research in the field of second language acquisition has looked at the presence of what have been labeled corrective recasts. This research has relied on the methodological practice of coding to identify particular turns as "corrective recasts." Often, the coding criteria make use of the notion of the maintenance of…
An upper bound on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2000-01-01
The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length.......The number of errors that a convolutional codes can correct in a segment of the encoded sequence is upper bounded by the number of distinct syndrome sequences of the relevant length....
Methodology for bus layout for topological quantum error correcting codes
Energy Technology Data Exchange (ETDEWEB)
Wosnitzka, Martin; Pedrocchi, Fabio L.; DiVincenzo, David P. [RWTH Aachen University, JARA Institute for Quantum Information, Aachen (Germany)
2016-12-15
Most quantum computing architectures can be realized as two-dimensional lattices of qubits that interact with each other. We take transmon qubits and transmission line resonators as promising candidates for qubits and couplers; we use them as basic building elements of a quantum code. We then propose a simple framework to determine the optimal experimental layout to realize quantum codes. We show that this engineering optimization problem can be reduced to the solution of standard binary linear programs. While solving such programs is a NP-hard problem, we propose a way to find scalable optimal architectures that require solving the linear program for a restricted number of qubits and couplers. We apply our methods to two celebrated quantum codes, namely the surface code and the Fibonacci code. (orig.)
Yan, Meng; Yao, Minyu; Zhang, Hongming
2005-11-01
The performance of a spectral-phase-encoded (SPE) optical code-division multiple-access (OCDMA) system is analyzed. Regarding the incorrectly decoded signal (IDS) as a nonstationary random process, we derive a novel probability distribution for it. The probability distribution of the IDS is considered a chi-squared distribution with degrees of freedom r=1, which is more reasonable and accurate than in previous work. The bit error rate (BER) of an SPE OCDMA system under multiple-access interference is evaluated. Numerical results show that the system can sustain very low BER even when there are multiple simultaneous users, and as the code length becomes longer or the initial pulse becomes shorter, the system performs better.
Upper bounds on the number of errors corrected by a convolutional code
DEFF Research Database (Denmark)
Justesen, Jørn
2004-01-01
We derive upper bounds on the weights of error patterns that can be corrected by a convolutional code with given parameters, or equivalently we give bounds on the code rate for a given set of error patterns. The bounds parallel the Hamming bound for block codes by relating the number of error...
Correct coding for laboratory procedures during assisted reproductive technology cycles.
2016-04-01
This document provides updated coding information for services related to assisted reproductive technology procedures. This document replaces the 2012 ASRM document of the same name. Copyright © 2016 American Society for Reproductive Medicine. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
GURJIT KAUR
2010-12-01
Full Text Available In this paper, an improved form of two dimensional optical orthogonal codes is introduced for optical CDMA system by using just six lasers. This new technique not only reduces the length of the code but also improves the bit error rate (BER performance of the system. The uniqueness of this coding architecture is that the two adjacent codes are not only different by their time slots but have different wavelength combination as well. The encoder and decoder structure has been designed with the help of filters and optical delay lines. An OCDMA system at 1 Gbps bit rate is designed for above codes and performance is evaluated and compared for various parameters i.e. number of simultaneous users, bit error rate, quality factor. The OCDMA system can accommodate 25 users for permissible BER of 10-9, with -15db received power at 1 Gbps bit rate respectively. If received power is kept low i.e. -22db, the OCDMA system can support 16 users with extremely low BER of 1.58e-41 for 1G bps bit rate.
Is a genome a codeword of an error-correcting code?
Directory of Open Access Journals (Sweden)
Luzinete C B Faria
Full Text Available Since a genome is a discrete sequence, the elements of which belong to a set of four letters, the question as to whether or not there is an error-correcting code underlying DNA sequences is unavoidable. The most common approach to answering this question is to propose a methodology to verify the existence of such a code. However, none of the methodologies proposed so far, although quite clever, has achieved that goal. In a recent work, we showed that DNA sequences can be identified as codewords in a class of cyclic error-correcting codes known as Hamming codes. In this paper, we show that a complete intron-exon gene, and even a plasmid genome, can be identified as a Hamming code codeword as well. Although this does not constitute a definitive proof that there is an error-correcting code underlying DNA sequences, it is the first evidence in this direction.
HCV IRES domain IIb affects the configuration of coding RNA in the 40S subunit's decoding groove.
Filbin, Megan E; Kieft, Jeffrey S
2011-07-01
Hepatitis C virus (HCV) uses a structured internal ribosome entry site (IRES) RNA to recruit the translation machinery to the viral RNA and begin protein synthesis without the ribosomal scanning process required for canonical translation initiation. Different IRES structural domains are used in this process, which begins with direct binding of the 40S ribosomal subunit to the IRES RNA and involves specific manipulation of the translational machinery. We have found that upon initial 40S subunit binding, the stem-loop domain of the IRES that contains the start codon unwinds and adopts a stable configuration within the subunit's decoding groove. This configuration depends on the sequence and structure of a different stem-loop domain (domain IIb) located far from the start codon in sequence, but spatially proximal in the IRES•40S complex. Mutation of domain IIb results in misconfiguration of the HCV RNA in the decoding groove that includes changes in the placement of the AUG start codon, and a substantial decrease in the ability of the IRES to initiate translation. Our results show that two distal regions of the IRES are structurally communicating at the initial step of 40S subunit binding and suggest that this is an important step in driving protein synthesis.
Error correction and degeneracy in surface codes suffering loss
International Nuclear Information System (INIS)
Stace, Thomas M.; Barrett, Sean D.
2010-01-01
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we give a detailed account of recent results in which we showed that topological quantum memories can simultaneously tolerate both loss errors and computational errors, with a graceful tradeoff between the threshold for each. We further discuss a number of subtleties that arise when implementing error correction on topological memories. We particularly focus on the role played by degeneracy in the matching algorithms and present a systematic study of its effects on thresholds. We also discuss some of the implications of degeneracy for estimating phase transition temperatures in the random bond Ising model.
Confidentiality of 2D Code using Infrared with Cell-level Error Correction
Directory of Open Access Journals (Sweden)
Nobuyuki Teraura
2013-03-01
Full Text Available Optical information media printed on paper use printing materials to absorb visible light. There is a 2D code, which may be encrypted but also can possibly be copied. Hence, we envisage an information medium that cannot possibly be copied and thereby offers high security. At the surface, the normal 2D code is printed. The inner layers consist of 2D codes printed using a variety of materials, which absorb certain distinct wavelengths, to form a multilayered 2D code. Information can be distributed among the 2D codes forming the inner layers of the multiplex. Additionally, error correction at cell level can be introduced.
Best linear decoding of random mask images
International Nuclear Information System (INIS)
Woods, J.W.; Ekstrom, M.P.; Palmieri, T.M.; Twogood, R.E.
1975-01-01
In 1968 Dicke proposed coded imaging of x and γ rays via random pinholes. Since then, many authors have agreed with him that this technique can offer significant image improvement. A best linear decoding of the coded image is presented, and its superiority over the conventional matched filter decoding is shown. Experimental results in the visible light region are presented. (U.S.)
Yeh, Pen-Shu (Inventor)
1998-01-01
A pre-coding method and device for improving data compression performance by removing correlation between a first original data set and a second original data set, each having M members, respectively. The pre-coding method produces a compression-efficiency-enhancing double-difference data set. The method and device produce a double-difference data set, i.e., an adjacent-delta calculation performed on a cross-delta data set or a cross-delta calculation performed on two adjacent-delta data sets, from either one of (1) two adjacent spectral bands coming from two discrete sources, respectively, or (2) two time-shifted data sets coming from a single source. The resulting double-difference data set is then coded using either a distortionless data encoding scheme (entropy encoding) or a lossy data compression scheme. Also, a post-decoding method and device for recovering a second original data set having been represented by such a double-difference data set.
Convolutional Encoder and Viterbi Decoder Using SOPC For Variable Constraint Length
DEFF Research Database (Denmark)
Kulkarni, Anuradha; Dnyaneshwar, Mantri; Prasad, Neeli R.
2013-01-01
Convolution encoder and Viterbi decoder are the basic and important blocks in any Code Division Multiple Accesses (CDMA). They are widely used in communication system due to their error correcting capability But the performance degrades with variable constraint length. In this context to have...... detailed analysis, this paper deals with the implementation of convolution encoder and Viterbi decoder using system on programming chip (SOPC). It uses variable constraint length of 7, 8 and 9 bits for 1/2 and 1/3 code rates. By analyzing the Viterbi algorithm it is seen that our algorithm has a better...
A Scalable Architecture of a Structured LDPC Decoder
Lee, Jason Kwok-San; Lee, Benjamin; Thorpe, Jeremy; Andrews, Kenneth; Dolinar, Sam; Hamkins, Jon
2004-01-01
We present a scalable decoding architecture for a certain class of structured LDPC codes. The codes are designed using a small (n,r) protograph that is replicated Z times to produce a decoding graph for a (Z x n, Z x r) code. Using this architecture, we have implemented a decoder for a (4096,2048) LDPC code on a Xilinx Virtex-II 2000 FPGA, and achieved decoding speeds of 31 Mbps with 10 fixed iterations. The implemented message-passing algorithm uses an optimized 3-bit non-uniform quantizer that operates with 0.2dB implementation loss relative to a floating point decoder.
Cooperative MIMO Communication at Wireless Sensor Network: An Error Correcting Code Approach
Islam, Mohammad Rakibul; Han, Young Shin
2011-01-01
Cooperative communication in wireless sensor network (WSN) explores the energy efficient wireless communication schemes between multiple sensors and data gathering node (DGN) by exploiting multiple input multiple output (MIMO) and multiple input single output (MISO) configurations. In this paper, an energy efficient cooperative MIMO (C-MIMO) technique is proposed where low density parity check (LDPC) code is used as an error correcting code. The rate of LDPC code is varied by varying the length of message and parity bits. Simulation results show that the cooperative communication scheme outperforms SISO scheme in the presence of LDPC code. LDPC codes with different code rates are compared using bit error rate (BER) analysis. BER is also analyzed under different Nakagami fading scenario. Energy efficiencies are compared for different targeted probability of bit error pb. It is observed that C-MIMO performs more efficiently when the targeted pb is smaller. Also the lower encoding rate for LDPC code offers better error characteristics. PMID:22163732
Mitsunaga, Erin M
2006-05-01
During the Korean War, International Business Machines (IBM) punch cards were created for every individual involved in military combat. Each card contained all pertinent personal information about the individual and was utilized to keep track of all soldiers involved. However, at present, all of the information known about these punch cards reveals only their format and their significance; there is little to no information on how these cards were created or how to interpret the information contained without the aid of the computer system used during the war. Today, it is believed there is no one available to explain this computerized system, nor do the original computers exist. This decode strategy is the result of an attempt to decipher the information on these cards through the use of all available medical and dental records for each individual examined. By cross-referencing the relevant personal information with the known format of the cards, a basic guess-and-check method was utilized. After examining hundreds of IBM punch cards, however, it has become clear that the punch card method of recording information was not infallible. In some cases, there are gaps of information on cards where there are data recorded on personal records; in others, information is punched incorrectly onto the cards, perhaps as the result of a transcription error. Taken all together, it is clear that the information contained on each individual's card should be taken solely as another form of personal documentation.
Xie, Jianwen; Douglas, Pamela K; Wu, Ying Nian; Brody, Arthur L; Anderson, Ariana E
2017-04-15
Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet other mathematical constraints provide alternate biologically-plausible frameworks for generating brain networks. Non-negative matrix factorization (NMF) would suppress negative BOLD signal by enforcing positivity. Spatial sparse coding algorithms (L1 Regularized Learning and K-SVD) would impose local specialization and a discouragement of multitasking, where the total observed activity in a single voxel originates from a restricted number of possible brain networks. The assumptions of independence, positivity, and sparsity to encode task-related brain networks are compared; the resulting brain networks within scan for different constraints are used as basis functions to encode observed functional activity. These encodings are then decoded using machine learning, by using the time series weights to predict within scan whether a subject is viewing a video, listening to an audio cue, or at rest, in 304 fMRI scans from 51 subjects. The sparse coding algorithm of L1 Regularized Learning outperformed 4 variations of ICA (pcoding algorithms. Holding constant the effect of the extraction algorithm, encodings using sparser spatial networks (containing more zero-valued voxels) had higher classification accuracy (pcoding algorithms suggests that algorithms which enforce sparsity, discourage multitasking, and promote local specialization may capture better the underlying source processes than those which allow inexhaustible local processes such as ICA. Negative BOLD signal may capture task-related activations. Copyright © 2017 Elsevier B.V. All rights reserved.
FPGA implementation of low complexity LDPC iterative decoder
Verma, Shivani; Sharma, Sanjay
2016-07-01
Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.
A novel approach to correct the coded aperture misalignment for fast neutron imaging
Energy Technology Data Exchange (ETDEWEB)
Zhang, F. N.; Hu, H. S., E-mail: huasi-hu@mail.xjtu.edu.cn; Wang, D. M.; Jia, J. [School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, T. K. [Laser Fusion Research Center, CAEP, Mianyang, 621900 Sichuan (China); Jia, Q. G. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)
2015-12-15
Aperture alignment is crucial for the diagnosis of neutron imaging because it has significant impact on the coding imaging and the understanding of the neutron source. In our previous studies on the neutron imaging system with coded aperture for large field of view, “residual watermark,” certain extra information that overlies reconstructed image and has nothing to do with the source is discovered if the peak normalization is employed in genetic algorithms (GA) to reconstruct the source image. Some studies on basic properties of residual watermark indicate that the residual watermark can characterize coded aperture and can thus be used to determine the location of coded aperture relative to the system axis. In this paper, we have further analyzed the essential conditions for the existence of residual watermark and the requirements of the reconstruction algorithm for the emergence of residual watermark. A gamma coded imaging experiment has been performed to verify the existence of residual watermark. Based on the residual watermark, a correction method for the aperture misalignment has been studied. A multiple linear regression model of the position of coded aperture axis, the position of residual watermark center, and the gray barycenter of neutron source with twenty training samples has been set up. Using the regression model and verification samples, we have found the position of the coded aperture axis relative to the system axis with an accuracy of approximately 20 μm. Conclusively, a novel approach has been established to correct the coded aperture misalignment for fast neutron coded imaging.
Elements of algebraic coding systems
Cardoso da Rocha, Jr, Valdemar
2014-01-01
Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...
LDPC Codes with Minimum Distance Proportional to Block Size
Divsalar, Dariush; Jones, Christopher; Dolinar, Samuel; Thorpe, Jeremy
2009-01-01
Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low
Portelli, Geoffrey; Barrett, John M; Hilgen, Gerrit; Masquelier, Timothée; Maccione, Alessandro; Di Marco, Stefano; Berdondini, Luca; Kornprobst, Pierre; Sernagor, Evelyne
2016-01-01
How a population of retinal ganglion cells (RGCs) encodes the visual scene remains an open question. Going beyond individual RGC coding strategies, results in salamander suggest that the relative latencies of a RGC pair encode spatial information. Thus, a population code based on this concerted spiking could be a powerful mechanism to transmit visual information rapidly and efficiently. Here, we tested this hypothesis in mouse by recording simultaneous light-evoked responses from hundreds of RGCs, at pan-retinal level, using a new generation of large-scale, high-density multielectrode array consisting of 4096 electrodes. Interestingly, we did not find any RGCs exhibiting a clear latency tuning to the stimuli, suggesting that in mouse, individual RGC pairs may not provide sufficient information. We show that a significant amount of information is encoded synergistically in the concerted spiking of large RGC populations. Thus, the RGC population response described with relative activities, or ranks, provides more relevant information than classical independent spike count- or latency- based codes. In particular, we report for the first time that when considering the relative activities across the whole population, the wave of first stimulus-evoked spikes is an accurate indicator of stimulus content. We show that this coding strategy coexists with classical neural codes, and that it is more efficient and faster. Overall, these novel observations suggest that already at the level of the retina, concerted spiking provides a reliable and fast strategy to rapidly transmit new visual scenes.
2016-08-24
to the seven-qubit Steane code [29] and also represents the smallest instance of a 2D topological color code [30]. Since the realized quantum error...Quantum Computations on a Topologically Encoded Qubit, Science 345, 302 (2014). [17] M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. D...Memory, J. Math . Phys. (N.Y.) 43, 4452 (2002). [20] B. M. Terhal, Quantum Error Correction for Quantum Memories, Rev. Mod. Phys. 87, 307 (2015). [21] D
SimCommSys: taking the errors out of error-correcting code simulations
Directory of Open Access Journals (Sweden)
Johann A. Briffa
2014-06-01
Full Text Available In this study, we present SimCommSys, a simulator of communication systems that we are releasing under an open source license. The core of the project is a set of C + + libraries defining communication system components and a distributed Monte Carlo simulator. Of principal interest is the error-control coding component, where various kinds of binary and non-binary codes are implemented, including turbo, LDPC, repeat-accumulate and Reed–Solomon. The project also contains a number of ready-to-build binaries implementing various stages of the communication system (such as the encoder and decoder, a complete simulator and a system benchmark. Finally, SimCommSys also provides a number of shell and python scripts to encapsulate routine use cases. As long as the required components are already available in SimCommSys, the user may simulate complete communication systems of their own design without any additional programming. The strict separation of development (needed only to implement new components and use (to simulate specific constructions encourages reproducibility of experimental work and reduces the likelihood of error. Following an overview of the framework, we provide some examples of how to use the framework, including the implementation of a simple codec, the specification of communication systems and their simulation.
Morikawa, Naoki; Tanaka, Toshihisa; Islam, Md Rabiul
2018-07-01
Mixed frequency and phase coding (FPC) can achieve the significant increase of the number of commands in steady-state visual evoked potential-based brain-computer interface (SSVEP-BCI). However, the inconsistent phases of the SSVEP over channels in a trial and the existence of non-contributing channels due to noise effects can decrease accurate detection of stimulus frequency. We propose a novel command detection method based on a complex sparse spatial filter (CSSF) by solving ℓ 1 - and ℓ 2,1 -regularization problems for a mixed-coded SSVEP-BCI. In particular, ℓ 2,1 -regularization (aka group sparsification) can lead to the rejection of electrodes that are not contributing to the SSVEP detection. A calibration data based canonical correlation analysis (CCA) and CSSF with ℓ 1 - and ℓ 2,1 -regularization cases were demonstrated for a 16-target stimuli with eleven subjects. The results of statistical test suggest that the proposed method with ℓ 1 - and ℓ 2,1 -regularization significantly achieved the highest ITR. The proposed approaches do not need any reference signals, automatically select prominent channels, and reduce the computational cost compared to the other mixed frequency-phase coding (FPC)-based BCIs. The experimental results suggested that the proposed method can be usable implementing BCI effectively with reduce visual fatigue. Copyright © 2018 Elsevier B.V. All rights reserved.
Sonea, Laura; Buse, Mihail; Gulei, Diana; Onaciu, Anca; Simon, Ioan; Braicu, Cornelia; Berindan-Neagoe, Ioana
2018-05-01
Lung cancer continues to be the leading topic concerning global mortality rate caused by can-cer; it needs to be further investigated to reduce these dramatic unfavorable statistic data. Non-coding RNAs (ncRNAs) have been shown to be important cellular regulatory factors and the alteration of their expression levels has become correlated to extensive number of pathologies. Specifically, their expres-sion profiles are correlated with development and progression of lung cancer, generating great interest for further investigation. This review focuses on the complex role of non-coding RNAs, namely miR-NAs, piwi-interacting RNAs, small nucleolar RNAs, long non-coding RNAs and circular RNAs in the process of developing novel biomarkers for diagnostic and prognostic factors that can then be utilized for personalized therapies toward this devastating disease. To support the concept of personalized medi-cine, we will focus on the roles of miRNAs in lung cancer tumorigenesis, their use as diagnostic and prognostic biomarkers and their application for patient therapy.
Corrections and additions to CONTEMPT-LT computer codes for containment analysis
International Nuclear Information System (INIS)
Eerikaeinen, Lauri.
1980-01-01
The report presents a new version of CONTEMPT-LT/26 tainment code. The corrections and additions are applicable also to other CONTEMPT-LT versions. Thermodynamical background of corrections are shortly described, and in addition, some essential points which should be taken into account in the analysis of a pressure suppression containment have been pointed out. The results obtained by the corrected version have been compared to those calculated by the original program, and to the measured data in the Marviken containment experiment No 10. Finally, it has been indicated that for reliable pressure suppression analysis a wide ranging condensation model for air-steam mixture is necessary. (author)
Reliable channel-adapted error correction: Bacon-Shor code recovery from amplitude damping
Á. Piedrafita (Álvaro); J.M. Renes (Joseph)
2017-01-01
textabstractWe construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
Czech Academy of Sciences Publication Activity Database
Gál, A.; Hansen, A. K.; Koucký, Michal; Pudlák, Pavel; Viola, E.
2013-01-01
Roč. 59, č. 10 (2013), s. 6611-6627 ISSN 0018-9448 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : bounded-depth circuits * error-correcting codes * hashing Subject RIV: BA - General Mathematics Impact factor: 2.650, year: 2013 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6578188
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
Czech Academy of Sciences Publication Activity Database
Gál, A.; Hansen, A. K.; Koucký, Michal; Pudlák, Pavel; Viola, E.
2013-01-01
Roč. 59, č. 10 (2013), s. 6611-6627 ISSN 0018-9448 R&D Projects: GA AV ČR IAA100190902 Institutional support: RVO:67985840 Keywords : bounded-depth circuits * error -correcting codes * hashing Subject RIV: BA - General Mathematics Impact factor: 2.650, year: 2013 http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6578188
Towards provably correct code generation for a hard real-time programming language
DEFF Research Database (Denmark)
Fränzle, Martin; Müller-Olm, Markus
1994-01-01
This paper sketches a hard real-time programming language featuring operators for expressing timeliness requirements in an abstract, implementation-independent way and presents parts of the design and verification of a provably correct code generator for that language. The notion of implementation...
Hogendoorn, Hinze; Burkitt, Anthony N
2018-05-01
Due to the delays inherent in neuronal transmission, our awareness of sensory events necessarily lags behind the occurrence of those events in the world. If the visual system did not compensate for these delays, we would consistently mislocalize moving objects behind their actual position. Anticipatory mechanisms that might compensate for these delays have been reported in animals, and such mechanisms have also been hypothesized to underlie perceptual effects in humans such as the Flash-Lag Effect. However, to date no direct physiological evidence for anticipatory mechanisms has been found in humans. Here, we apply multivariate pattern classification to time-resolved EEG data to investigate anticipatory coding of object position in humans. By comparing the time-course of neural position representation for objects in both random and predictable apparent motion, we isolated anticipatory mechanisms that could compensate for neural delays when motion trajectories were predictable. As well as revealing an early neural position representation (lag 80-90 ms) that was unaffected by the predictability of the object's trajectory, we demonstrate a second neural position representation at 140-150 ms that was distinct from the first, and that was pre-activated ahead of the moving object when it moved on a predictable trajectory. The latency advantage for predictable motion was approximately 16 ± 2 ms. To our knowledge, this provides the first direct experimental neurophysiological evidence of anticipatory coding in human vision, revealing the time-course of predictive mechanisms without using a spatial proxy for time. The results are numerically consistent with earlier animal work, and suggest that current models of spatial predictive coding in visual cortex can be effectively extended into the temporal domain. Copyright © 2018 Elsevier Inc. All rights reserved.
Interior point decoding for linear vector channels
International Nuclear Information System (INIS)
Wadayama, T
2008-01-01
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter-symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem
Interior point decoding for linear vector channels
Energy Technology Data Exchange (ETDEWEB)
Wadayama, T [Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya, Aichi, 466-8555 (Japan)], E-mail: wadayama@nitech.ac.jp
2008-01-15
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector channels include many practically important channels such as inter-symbol interference channels and partial response channels. It is shown that the maximum likelihood decoding (MLD) rule for a linear vector channel can be relaxed to a convex optimization problem, which is called a relaxed MLD problem.
LDPC Decoding on GPU for Mobile Device
Directory of Open Access Journals (Sweden)
Yiqin Lu
2016-01-01
Full Text Available A flexible software LDPC decoder that exploits data parallelism for simultaneous multicode words decoding on the mobile device is proposed in this paper, supported by multithreading on OpenCL based graphics processing units. By dividing the check matrix into several parts to make full use of both the local memory and private memory on GPU and properly modify the code capacity each time, our implementation on a mobile phone shows throughputs above 100 Mbps and delay is less than 1.6 millisecond in decoding, which make high-speed communication like video calling possible. To realize efficient software LDPC decoding on the mobile device, the LDPC decoding feature on communication baseband chip should be replaced to save the cost and make it easier to upgrade decoder to be compatible with a variety of channel access schemes.
DEFF Research Database (Denmark)
Rakêt, Lars Lau; Søgaard, Jacob; Salmistraro, Matteo
2012-01-01
We consider Distributed Video Coding (DVC) in presence of communication errors. First, we present DVC side information generation based on a new method of optical flow driven frame interpolation, where a highly optimized TV-L1 algorithm is used for the flow calculations and combine three flows....... Thereafter methods for exploiting the error-correcting capabilities of the LDPCA code in DVC are investigated. The proposed frame interpolation includes a symmetric flow constraint to the standard forward-backward frame interpolation scheme, which improves quality and handling of large motion. The three...... flows are combined in one solution. The proposed frame interpolation method consistently outperforms an overlapped block motion compensation scheme and a previous TV-L1 optical flow frame interpolation method with an average PSNR improvement of 1.3 dB and 2.3 dB respectively. For a GOP size of 2...
Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection
Meng, Jiahui; Zhao, Danfeng; Tian, Hai; Zhang, Liang
2018-01-01
In order to improve the performance of non-binary low-density parity check codes (LDPC) hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA) and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes’ (VN) magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF) algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER) of 10−5 over an additive white Gaussian noise (AWGN) channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced. PMID:29342963
Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection.
Meng, Jiahui; Zhao, Danfeng; Tian, Hai; Zhang, Liang
2018-01-15
In order to improve the performance of non-binary low-density parity check codes (LDPC) hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA) and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes' (VN) magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF) algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER) of 10 -5 over an additive white Gaussian noise (AWGN) channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced.
Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection
Directory of Open Access Journals (Sweden)
Jiahui Meng
2018-01-01
Full Text Available In order to improve the performance of non-binary low-density parity check codes (LDPC hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes’ (VN magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER of 10−5 over an additive white Gaussian noise (AWGN channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced.
Telemetry advances in data compression and channel coding
Miller, Warner H.; Morakis, James C.; Yeh, Pen-Shu
1990-01-01
Addressed in this paper is the dependence of telecommunication channel, forward error correcting coding and source data compression coding on integrated circuit technology. Emphasis is placed on real time high speed Reed Solomon (RS) decoding using full custom VLSI technology. Performance curves of NASA's standard channel coder and a proposed standard lossless data compression coder are presented.
Cooperative MIMO communication at wireless sensor network: an error correcting code approach.
Islam, Mohammad Rakibul; Han, Young Shin
2011-01-01
Cooperative communication in wireless sensor network (WSN) explores the energy efficient wireless communication schemes between multiple sensors and data gathering node (DGN) by exploiting multiple input multiple output (MIMO) and multiple input single output (MISO) configurations. In this paper, an energy efficient cooperative MIMO (C-MIMO) technique is proposed where low density parity check (LDPC) code is used as an error correcting code. The rate of LDPC code is varied by varying the length of message and parity bits. Simulation results show that the cooperative communication scheme outperforms SISO scheme in the presence of LDPC code. LDPC codes with different code rates are compared using bit error rate (BER) analysis. BER is also analyzed under different Nakagami fading scenario. Energy efficiencies are compared for different targeted probability of bit error p(b). It is observed that C-MIMO performs more efficiently when the targeted p(b) is smaller. Also the lower encoding rate for LDPC code offers better error characteristics.
A Survey of Progress in Coding Theory in the Soviet Union. Final Report.
Kautz, William H.; Levitt, Karl N.
The results of a comprehensive technical survey of all published Soviet literature in coding theory and its applications--over 400 papers and books appearing before March 1967--are described in this report. Noteworthy Soviet contributions are discussed, including codes for the noiseless channel, codes that correct asymetric errors, decoding for…
Futur d'une infrastructure de correction automatisée : CodeGradX
Queinnec , Christian; Pons , Olivier
2016-01-01
Cet article évoque quelques expériences et nouvelles idées au-tour d'une infrastructure de correction automatisée de programmes. CodeGradX est une infrastructure de correction automatisée de programmes. Elle est en service depuis 2008 (initialement sous le nom de FW4EX) et a depuis corrigé plus de 150 000 soumissions d'étudiants à des exercices principalement en Scheme, utilitaires d'Unix, JavaScript mais aussi en C, Octave, O'Caml, Python sans oublier les compétitions annuelles des Journées ...
Timing group delay and differential code bias corrections for BeiDou positioning
Guo, Fei; Zhang, Xiaohong; Wang, Jinling
2015-05-01
This article first clearly figures out the relationship between parameters of timing group delay (TGD) and differential code bias (DCB) for BDS, and demonstrates the equivalence of TGD and DCB correction models combining theory with practice. The TGD/DCB correction models have been extended to various occasions for BDS positioning, and such models have been evaluated by real triple-frequency datasets. To test the effectiveness of broadcast TGDs in the navigation message and DCBs provided by the Multi-GNSS Experiment (MGEX), both standard point positioning (SPP) and precise point positioning (PPP) tests are carried out for BDS signals with different schemes. Furthermore, the influence of differential code biases on BDS positioning estimates such as coordinates, receiver clock biases, tropospheric delays and carrier phase ambiguities is investigated comprehensively. Comparative analysis show that the unmodeled differential code biases degrade the performance of BDS SPP by a factor of two or more, whereas the estimates of PPP are subject to varying degrees of influences. For SPP, the accuracy of dual-frequency combinations is slightly worse than that of single-frequency, and they are much more sensitive to the differential code biases, particularly for the B2B3 combination. For PPP, the uncorrected differential code biases are mostly absorbed into the receiver clock bias and carrier phase ambiguities and thus resulting in a much longer convergence time. Even though the influence of the differential code biases could be mitigated over time and comparable positioning accuracy could be achieved after convergence, it is suggested to properly handle with the differential code biases since it is vital for PPP convergence and integer ambiguity resolution.
Directory of Open Access Journals (Sweden)
Nicolai Lang, Hans Peter Büchler
2018-01-01
Full Text Available Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.
Links between N-modular redundancy and the theory of error-correcting codes
Bobin, V.; Whitaker, S.; Maki, G.
1992-01-01
N-Modular Redundancy (NMR) is one of the best known fault tolerance techniques. Replication of a module to achieve fault tolerance is in some ways analogous to the use of a repetition code where an information symbol is replicated as parity symbols in a codeword. Linear Error-Correcting Codes (ECC) use linear combinations of information symbols as parity symbols which are used to generate syndromes for error patterns. These observations indicate links between the theory of ECC and the use of hardware redundancy for fault tolerance. In this paper, we explore some of these links and show examples of NMR systems where identification of good and failed elements is accomplished in a manner similar to error correction using linear ECC's.
Zhou, Ke-Ren; Liu, Shun; Sun, Wen-Ju; Zheng, Ling-Ling; Zhou, Hui; Yang, Jian-Hua; Qu, Liang-Hu
2017-01-04
The abnormal transcriptional regulation of non-coding RNAs (ncRNAs) and protein-coding genes (PCGs) is contributed to various biological processes and linked with human diseases, but the underlying mechanisms remain elusive. In this study, we developed ChIPBase v2.0 (http://rna.sysu.edu.cn/chipbase/) to explore the transcriptional regulatory networks of ncRNAs and PCGs. ChIPBase v2.0 has been expanded with ∼10 200 curated ChIP-seq datasets, which represent about 20 times expansion when comparing to the previous released version. We identified thousands of binding motif matrices and their binding sites from ChIP-seq data of DNA-binding proteins and predicted millions of transcriptional regulatory relationships between transcription factors (TFs) and genes. We constructed 'Regulator' module to predict hundreds of TFs and histone modifications that were involved in or affected transcription of ncRNAs and PCGs. Moreover, we built a web-based tool, Co-Expression, to explore the co-expression patterns between DNA-binding proteins and various types of genes by integrating the gene expression profiles of ∼10 000 tumor samples and ∼9100 normal tissues and cell lines. ChIPBase also provides a ChIP-Function tool and a genome browser to predict functions of diverse genes and visualize various ChIP-seq data. This study will greatly expand our understanding of the transcriptional regulations of ncRNAs and PCGs. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
DEFF Research Database (Denmark)
Gal, A.; Hansen, Kristoffer Arnsfelt; Koucky, Michal
2013-01-01
We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1}Ω(n)→{0,1}n with minimum distance Ω(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: 1) if d=2, then w=Θ(n (lgn/lglgn)2); 2) if d=3, then w...
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
DEFF Research Database (Denmark)
Gál, Anna; Hansen, Kristoffer Arnsfelt; Koucký, Michal
2012-01-01
We bound the minimum number w of wires needed to compute any (asymptotically good) error-correcting code C:{0,1}Ω(n) -> {0,1}n with minimum distance Ω(n), using unbounded fan-in circuits of depth d with arbitrary gates. Our main results are: (1) If d=2 then w = Θ(n ({log n/ log log n})2). (2) If d...
What Information is Stored in DNA: Does it Contain Digital Error Correcting Codes?
Liebovitch, Larry
1998-03-01
evidence for such error correcting codes in these genes. However, we analyzed only a small amount of DNA and if digitial error correcting schemes are present in DNA, they may be more subtle than such simple linear block codes. The basic issue we raise here, is how information is stored in DNA and an appreciation that digital symbol sequences, such as DNA, admit of interesting schemes to store and protect the fidelity of their information content. Liebovitch, Tao, Todorov, Levine. 1996. Biophys. J. 71:1539-1544. Supported by NIH grant EY6234.
Multi-shape pulse pile-up correction: The MCPPU code
International Nuclear Information System (INIS)
Sabbatucci, Lorenzo; Scot, Viviana; Fernandez, Jorge E.
2014-01-01
In spectroscopic measurements with high counting rate, pulse pile-up (PPU) is a common distortion of the spectrum. It is fully ascribable to the pulse handling circuitry of the detector and it is not comprised in the detector response function which is well explained by a purely physical model. Since PPU occurs after the transport inside the detector, this is the first correction to perform in case of spectrum unfolding. Many producers include electronic rejection circuits to limit the appearance of PPU, but it is never suppressed completely. Therefore, it is always necessary to correct PPU distortions after the measurement. In the present work, it is described the post-processing tool MCPPU (Monte Carlo Pulse Pile-Up), based on the MC algorithm developed by Guo et al. (2004, 2005). MCPPU automatically determines the dead time of the counting system and corrects for PPU effects even in the presence of electronic suppression. The capability of allowing a user defined pulse shape makes the code suitable to be used with any kind of detector. The features of MCPPU are illustrated with some examples. - Highlights: • Pulse pile-up (PPU) is a common distortion in radiation detection. • MCPPU is a Monte Carlo code to perform post-processing PPU correction. • MCPPU evaluates automatically the dead time to use in the pile-up recovery. • The measured pulse shape can be introduced as a normalized discrete distribution. • MCPPU is compatible with detectors using electronic rejection circuitry
Image authentication using distributed source coding.
Lin, Yao-Chung; Varodayan, David; Girod, Bernd
2012-01-01
We present a novel approach using distributed source coding for image authentication. The key idea is to provide a Slepian-Wolf encoded quantized image projection as authentication data. This version can be correctly decoded with the help of an authentic image as side information. Distributed source coding provides the desired robustness against legitimate variations while detecting illegitimate modification. The decoder incorporating expectation maximization algorithms can authenticate images which have undergone contrast, brightness, and affine warping adjustments. Our authentication system also offers tampering localization by using the sum-product algorithm.
DEFF Research Database (Denmark)
Lassen, Mikael Østergaard; Sabuncu, Metin; Huck, Alexander
2010-01-01
A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code that robustly protects the involved fragile quantum states from their environment. Just as classical error-correcting codes are indispensible in today's information...... technologies, it is believed that quantum error-correcting code will play a similarly crucial role in tomorrow's quantum information systems. Here, we report on the experimental demonstration of a quantum erasure-correcting code that overcomes the devastating effect of photon losses. Our quantum code is based...... on linear optics, and it protects a four-mode entangled mesoscopic state of light against erasures. We investigate two approaches for circumventing in-line losses, and demonstrate that both approaches exhibit transmission fidelities beyond what is possible by classical means. Because in-line attenuation...
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
Energy Technology Data Exchange (ETDEWEB)
Pastawski, Fernando; Yoshida, Beni [Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics,California Institute of Technology,1200 E. California Blvd., Pasadena CA 91125 (United States); Harlow, Daniel [Princeton Center for Theoretical Science, Princeton University,400 Jadwin Hall, Princeton NJ 08540 (United States); Preskill, John [Institute for Quantum Information & Matter and Walter Burke Institute for Theoretical Physics,California Institute of Technology,1200 E. California Blvd., Pasadena CA 91125 (United States)
2015-06-23
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in http://dx.doi.org/10.1007/JHEP04(2015)163.
Multiple component codes based generalized LDPC codes for high-speed optical transport.
Djordjevic, Ivan B; Wang, Ting
2014-07-14
A class of generalized low-density parity-check (GLDPC) codes suitable for optical communications is proposed, which consists of multiple local codes. It is shown that Hamming, BCH, and Reed-Muller codes can be used as local codes, and that the maximum a posteriori probability (MAP) decoding of these local codes by Ashikhmin-Lytsin algorithm is feasible in terms of complexity and performance. We demonstrate that record coding gains can be obtained from properly designed GLDPC codes, derived from multiple component codes. We then show that several recently proposed classes of LDPC codes such as convolutional and spatially-coupled codes can be described using the concept of GLDPC coding, which indicates that the GLDPC coding can be used as a unified platform for advanced FEC enabling ultra-high speed optical transport. The proposed class of GLDPC codes is also suitable for code-rate adaption, to adjust the error correction strength depending on the optical channel conditions.
Bilayer expurgated LDPC codes with uncoded relaying
Directory of Open Access Journals (Sweden)
Md. Noor-A-Rahim
2017-08-01
Full Text Available Bilayer low-density parity-check (LDPC codes are an effective coding technique for decode-and-forward relaying, where the relay forwards extra parity bits to help the destination to decode the source bits correctly. In the existing bilayer coding scheme, these parity bits are protected by an error correcting code and assumed reliably available at the receiver. We propose an uncoded relaying scheme, where the extra parity bits are forwarded to the destination without any protection. Through density evolution analysis and simulation results, we show that our proposed scheme achieves better performance in terms of bit erasure probability than the existing relaying scheme. In addition, our proposed scheme results in lower complexity at the relay.
Coded Modulation in C and MATLAB
Hamkins, Jon; Andrews, Kenneth S.
2011-01-01
This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations.
Quantum states and their marginals. From multipartite entanglement to quantum error-correcting codes
International Nuclear Information System (INIS)
Huber, Felix Michael
2017-01-01
At the heart of the curious phenomenon of quantum entanglement lies the relation between the whole and its parts. In my thesis, I explore different aspects of this theme in the multipartite setting by drawing connections to concepts from statistics, graph theory, and quantum error-correcting codes: first, I address the case when joint quantum states are determined by their few-body parts and by Jaynes' maximum entropy principle. This can be seen as an extension of the notion of entanglement, with less complex states already being determined by their few-body marginals. Second, I address the conditions for certain highly entangled multipartite states to exist. In particular, I present the solution of a long-standing open problem concerning the existence of an absolutely maximally entangled state on seven qubits. This sheds light on the algebraic properties of pure quantum states, and on the conditions that constrain the sharing of entanglement amongst multiple particles. Third, I investigate Ulam's graph reconstruction problems in the quantum setting, and obtain legitimacy conditions of a set of states to be the reductions of a joint graph state. Lastly, I apply and extend the weight enumerator machinery from quantum error correction to investigate the existence of codes and highly entangled states in higher dimensions. This clarifies the physical interpretation of the weight enumerators and of the quantum MacWilliams identity, leading to novel applications in multipartite entanglement.
Calculations of electron fluence correction factors using the Monte Carlo code PENELOPE
International Nuclear Information System (INIS)
Siegbahn, E A; Nilsson, B; Fernandez-Varea, J M; Andreo, P
2003-01-01
In electron-beam dosimetry, plastic phantom materials may be used instead of water for the determination of absorbed dose to water. A correction factor φ water plastic is then needed for converting the electron fluence in the plastic phantom to the fluence at an equivalent depth in water. The recommended values for this factor given by AAPM TG-25 (1991 Med. Phys. 18 73-109) and the IAEA protocols TRS-381 (1997) and TRS-398 (2000) disagree, in particular at large depths. Calculations of the electron fluence have been done, using the Monte Carlo code PENELOPE, in semi-infinite phantoms of water and common plastic materials (PMMA, clear polystyrene, A-150, polyethylene, Plastic water TM and Solid water TM (WT1)). The simulations have been carried out for monoenergetic electron beams of 6, 10 and 20 MeV, as well as for a realistic clinical beam. The simulated fluence correction factors differ from the values in the AAPM and IAEA recommendations by up to 2%, and are in better agreement with factors obtained by Ding et al (1997 Med. Phys. 24 161-76) using EGS4. Our Monte Carlo calculations are also in good accordance with φ water plastic values measured by using an almost perturbation-free ion chamber. The important interdependence between depth- and fluence-scaling corrections for plastic phantoms is discussed. Discrepancies between the measured and the recommended values of φ water plastic may then be explained considering the different depth-scaling rules used
An overview of turbo decoding on fading channels
ATILGAN, Doğan
2009-01-01
A review of turbo coding and decoding has been presented in the literature [1]. In that paper, turbo coding and decoding on AWGN (Additive White Gaussian Noise) channels has been elaborated. In wireless communications, a phenomennon called multipath fading is frequently encountered. Therefore, investigation of efficient techniques to tackle with the destructive effects of fading is essential. Turbo coding has been proven as an efficient channel coding technique for AWGN channels. Some of the ...
DEFF Research Database (Denmark)
Pinkevych, Mykola; Cromer, Deborah; Tolstrup, Martin
2016-01-01
[This corrects the article DOI: 10.1371/journal.ppat.1005000.][This corrects the article DOI: 10.1371/journal.ppat.1005740.][This corrects the article DOI: 10.1371/journal.ppat.1005679.].......[This corrects the article DOI: 10.1371/journal.ppat.1005000.][This corrects the article DOI: 10.1371/journal.ppat.1005740.][This corrects the article DOI: 10.1371/journal.ppat.1005679.]....
Directory of Open Access Journals (Sweden)
Dan Tulpan
2013-01-01
Full Text Available This paper presents a novel hybrid DNA encryption (HyDEn approach that uses randomized assignments of unique error-correcting DNA Hamming code words for single characters in the extended ASCII set. HyDEn relies on custom-built quaternary codes and a private key used in the randomized assignment of code words and the cyclic permutations applied on the encoded message. Along with its ability to detect and correct errors, HyDEn equals or outperforms existing cryptographic methods and represents a promising in silico DNA steganographic approach.
Zhang, Guangzhi; Cai, Shaobin; Xiong, Naixue
2018-02-03
One of the remarkable challenges about Wireless Sensor Networks (WSN) is how to transfer the collected data efficiently due to energy limitation of sensor nodes. Network coding will increase network throughput of WSN dramatically due to the broadcast nature of WSN. However, the network coding usually propagates a single original error over the whole network. Due to the special property of error propagation in network coding, most of error correction methods cannot correct more than C /2 corrupted errors where C is the max flow min cut of the network. To maximize the effectiveness of network coding applied in WSN, a new error-correcting mechanism to confront the propagated error is urgently needed. Based on the social network characteristic inherent in WSN and L1 optimization, we propose a novel scheme which successfully corrects more than C /2 corrupted errors. What is more, even if the error occurs on all the links of the network, our scheme also can correct errors successfully. With introducing a secret channel and a specially designed matrix which can trap some errors, we improve John and Yi's model so that it can correct the propagated errors in network coding which usually pollute exactly 100% of the received messages. Taking advantage of the social characteristic inherent in WSN, we propose a new distributed approach that establishes reputation-based trust among sensor nodes in order to identify the informative upstream sensor nodes. With referred theory of social networks, the informative relay nodes are selected and marked with high trust value. The two methods of L1 optimization and utilizing social characteristic coordinate with each other, and can correct the propagated error whose fraction is even exactly 100% in WSN where network coding is performed. The effectiveness of the error correction scheme is validated through simulation experiments.
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
International Nuclear Information System (INIS)
Bravyi, Sergey; Terhal, Barbara
2009-01-01
We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of size O(1). Our first result concerns the optimal scaling of the distance d with the linear size of the lattice L. We prove an upper bound d=O(L D-1 ) which is tight for D=1, 2. This bound applies to both subspace and subsystem stabilizer codes. Secondly, we analyze the suitability of stabilizer codes for building a self-correcting quantum memory. Any stabilizer code with geometrically local generators can be naturally transformed to a local Hamiltonian penalizing states that violate the stabilizer condition. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of the code. We prove that for D=1, 2, different logical states can be mapped into each other by a sequence of single-qubit Pauli errors such that the energy of all intermediate states is upper bounded by a constant independent of the lattice size L. The same result holds if there are unused logical qubits that are treated as 'gauge qubits'. It demonstrates that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1, 2. This result is in sharp contrast with the existence of a classical self-correcting memory in the form of a two-dimensional (2D) ferromagnet. Our results leave open the possibility for a self-correcting quantum memory based on 2D subsystem codes or on 3D subspace or subsystem codes.
Image coding based on maximum entropy partitioning for identifying ...
Indian Academy of Sciences (India)
A new coding scheme based on maximum entropy partitioning is proposed in our work, particularly to identify the improbable intensities related to different emotions. The improbable intensities when used as a mask decode the facial expression correctly, providing an effectiveplatform for future emotion categorization ...
LDPC-based iterative joint source-channel decoding for JPEG2000.
Pu, Lingling; Wu, Zhenyu; Bilgin, Ali; Marcellin, Michael W; Vasic, Bane
2007-02-01
A framework is proposed for iterative joint source-channel decoding of JPEG2000 codestreams. At the encoder, JPEG2000 is used to perform source coding with certain error-resilience (ER) modes, and LDPC codes are used to perform channel coding. During decoding, the source decoder uses the ER modes to identify corrupt sections of the codestream and provides this information to the channel decoder. Decoding is carried out jointly in an iterative fashion. Experimental results indicate that the proposed method requires fewer iterations and improves overall system performance.
Bidirectional Fano Algorithm for Lattice Coded MIMO Channels
Al-Quwaiee, Hessa
2013-01-01
channel model. Channel codes based on lattices are preferred due to three facts: lattice codes have simple structure, the code can achieve the limits of the channel, and they can be decoded efficiently using lattice decoders which can be considered
FPGA implementation of high-performance QC-LDPC decoder for optical communications
Zou, Ding; Djordjevic, Ivan B.
2015-01-01
Forward error correction is as one of the key technologies enabling the next-generation high-speed fiber optical communications. Quasi-cyclic (QC) low-density parity-check (LDPC) codes have been considered as one of the promising candidates due to their large coding gain performance and low implementation complexity. In this paper, we present our designed QC-LDPC code with girth 10 and 25% overhead based on pairwise balanced design. By FPGAbased emulation, we demonstrate that the 5-bit soft-decision LDPC decoder can achieve 11.8dB net coding gain with no error floor at BER of 10-15 avoiding using any outer code or post-processing method. We believe that the proposed single QC-LDPC code is a promising solution for 400Gb/s optical communication systems and beyond.
Recent advances in coding theory for near error-free communications
Cheung, K.-M.; Deutsch, L. J.; Dolinar, S. J.; Mceliece, R. J.; Pollara, F.; Shahshahani, M.; Swanson, L.
1991-01-01
Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.
Quantum BCH Codes Based on Spectral Techniques
International Nuclear Information System (INIS)
Guo Ying; Zeng Guihua
2006-01-01
When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F 2 , which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.
Optimal Codes for the Burst Erasure Channel
Hamkins, Jon
2010-01-01
Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure
Vectorization of Reed Solomon decoding and mapping on the EVP
Kumar, A.; Berkel, van C.H.
2008-01-01
Reed Solomon (RS) codes are used in a variety of (wireless) communication systems. Although commonly implemented in dedicated hardware, this paper explores the mapping of high-throughput RS decoding on vector DSPs. The four modules of such a decoder, viz. Syndrome Computation, Key Equation Solver,
Photonic entanglement-assisted quantum low-density parity-check encoders and decoders.
Djordjevic, Ivan B
2010-05-01
I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.
Mapping visual stimuli to perceptual decisions via sparse decoding of mesoscopic neural activity.
Sajda, Paul
2010-01-01
In this talk I will describe our work investigating sparse decoding of neural activity, given a realistic mapping of the visual scene to neuronal spike trains generated by a model of primary visual cortex (V1). We use a linear decoder which imposes sparsity via an L1 norm. The decoder can be viewed as a decoding neuron (linear summation followed by a sigmoidal nonlinearity) in which there are relatively few non-zero synaptic weights. We find: (1) the best decoding performance is for a representation that is sparse in both space and time, (2) decoding of a temporal code results in better performance than a rate code and is also a better fit to the psychophysical data, (3) the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases, with as little as 1% of the neurons required for decoding at the highest signal-to-noise levels, and (4) sparse decoding results in a more accurate decoding of the stimulus and is a better fit to psychophysical performance than a distributed decoding, for example one imposed by an L2 norm. We conclude that sparse coding is well-justified from a decoding perspective in that it results in a minimum number of neurons and maximum accuracy when sparse representations can be decoded from the neural dynamics.
EXIT Chart Analysis of Binary Message-Passing Decoders
DEFF Research Database (Denmark)
Lechner, Gottfried; Pedersen, Troels; Kramer, Gerhard
2007-01-01
Binary message-passing decoders for LDPC codes are analyzed using EXIT charts. For the analysis, the variable node decoder performs all computations in the L-value domain. For the special case of a hard decision channel, this leads to the well know Gallager B algorithm, while the analysis can...... be extended to channels with larger output alphabets. By increasing the output alphabet from hard decisions to four symbols, a gain of more than 1.0 dB is achieved using optimized codes. For this code optimization, the mixing property of EXIT functions has to be modified to the case of binary message......-passing decoders....
A transient, Hex-Z nodal code corrected by discontinuity factors
International Nuclear Information System (INIS)
Shatilla, Y.A.M.; Henry, A.F.
1993-01-01
This document constitutes Volume 1 of the Final Report of a three-year study supported by the special Research Grant Program for Nuclear Energy Research set up by the US Department of Energy. The original motivation for the work was to provide a fast and accurate computer program for the analysis of transients in heavy water or graphite-moderated reactors being considered as candidates for the New Production Reactor. Thus, part of the funding was by way of pass-through money from the Savannah River Laboratory. With this intent in mind, a three-dimensional (Hex-Z), general-energy-group transient, nodal code was created, programmed, and tested. In order to improve accuracy, correction terms, called open-quotes discontinuity factors,close quotes were incorporated into the nodal equations. Ideal values of these factors force the nodal equations to provide node-integrated reaction rates and leakage rates across nodal surfaces that match exactly those edited from a more exact reference calculation. Since the exact reference solution is needed to compute the ideal discontinuity factors, the fact that they result in exact nodal equations would be of little practical interest were it not that approximate discontinuity factors, found at a greatly reduced cost, often yield very accurate results. For example, for light-water reactors, discontinuity factors found from two-dimensional, fine-mesh, multigroup transport solutions for two-dimensional cuts of a fuel assembly provide very accurate predictions of three-dimensional, full-core power distributions. The present document (volume 1) deals primarily with the specification, programming and testing of the three-dimensional, Hex-Z computer program. The program solves both the static (eigenvalue) and transient, general-energy-group, nodal equations corrected by user-supplied discontinuity factors
The application of LDPC code in MIMO-OFDM system
Liu, Ruian; Zeng, Beibei; Chen, Tingting; Liu, Nan; Yin, Ninghao
2018-03-01
The combination of MIMO and OFDM technology has become one of the key technologies of the fourth generation mobile communication., which can overcome the frequency selective fading of wireless channel, increase the system capacity and improve the frequency utilization. Error correcting coding introduced into the system can further improve its performance. LDPC (low density parity check) code is a kind of error correcting code which can improve system reliability and anti-interference ability, and the decoding is simple and easy to operate. This paper mainly discusses the application of LDPC code in MIMO-OFDM system.
On Lattice Sequential Decoding for The Unconstrained AWGN Channel
Abediseid, Walid
2013-04-04
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the \\\\textit{lattice decoder}. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter --- the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.
On Lattice Sequential Decoding for The Unconstrained AWGN Channel
Abediseid, Walid
2012-10-01
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter --- the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.
On Lattice Sequential Decoding for The Unconstrained AWGN Channel
Abediseid, Walid; Alouini, Mohamed-Slim
2012-01-01
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter --- the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.
Forms and Linear Network Codes
DEFF Research Database (Denmark)
Hansen, Johan P.
We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is inspired by the methods of the author utilizing the osculating...... spaces of Veronese varieties. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The vector spaces in our construction are equidistant in the above metric and the distance between any pair of vector spaces is large making...
Adaptive decoding of MPEG-4 sprites for memory-constrained embedded systems
Pastrnak, M.; Farin, D.S.; With, de P.H.N.; Cardinal, J.; Cerf, N.; Delgrnage, O.
2005-01-01
Background sprite decoding is an essential part of object-based video coding.The composition and rendering of a final scene involves the placing of individual video objects in a predefined way superimposed on the decoded background image. The MPEG-4 standard includes the decoding algorithm for
Han, Sangkwon; Bae, Hyung Jong; Kim, Junhoi; Shin, Sunghwan; Choi, Sung-Eun; Lee, Sung Hoon; Kwon, Sunghoon; Park, Wook
2012-11-20
A QR-coded microtaggant for the anti-counterfeiting of drugs is proposed that can provide high capacity and error-correction capability. It is fabricated lithographically in a microfluidic channel with special consideration of the island patterns in the QR Code. The microtaggant is incorporated in the drug capsule ("on-dose authentication") and can be read by a simple smartphone QR Code reader application when removed from the capsule and washed free of drug. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Construction of Short-Length High-Rates LDPC Codes Using Difference Families
Directory of Open Access Journals (Sweden)
Deny Hamdani
2010-10-01
Full Text Available Low-density parity-check (LDPC code is linear-block error-correcting code defined by sparse parity-check matrix. It is decoded using the massage-passing algorithm, and in many cases, capable of outperforming turbo code. This paper presents a class of low-density parity-check (LDPC codes showing good performance with low encoding complexity. The code is constructed using difference families from combinatorial design. The resulting code, which is designed to have short code length and high code rate, can be encoded with low complexity due to its quasi-cyclic structure, and performs well when it is iteratively decoded with the sum-product algorithm. These properties of LDPC code are quite suitable for applications in future wireless local area network.
Adaptive Combined Source and Channel Decoding with Modulation ...
African Journals Online (AJOL)
In this paper, an adaptive system employing combined source and channel decoding with modulation is proposed for slow Rayleigh fading channels. Huffman code is used as the source code and Convolutional code is used for error control. The adaptive scheme employs a family of Convolutional codes of different rates ...
Directory of Open Access Journals (Sweden)
T. Kalavathi Devi
2015-01-01
Full Text Available Convolutional codes are comprehensively used as Forward Error Correction (FEC codes in digital communication systems. For decoding of convolutional codes at the receiver end, Viterbi decoder is often used to have high priority. This decoder meets the demand of high speed and low power. At present, the design of a competent system in Very Large Scale Integration (VLSI technology requires these VLSI parameters to be finely defined. The proposed asynchronous method focuses on reducing the power consumption of Viterbi decoder for various constraint lengths using asynchronous modules. The asynchronous designs are based on commonly used Quasi Delay Insensitive (QDI templates, namely, Precharge Half Buffer (PCHB and Weak Conditioned Half Buffer (WCHB. The functionality of the proposed asynchronous design is simulated and verified using Tanner Spice (TSPICE in 0.25 µm, 65 nm, and 180 nm technologies of Taiwan Semiconductor Manufacture Company (TSMC. The simulation result illustrates that the asynchronous design techniques have 25.21% of power reduction compared to synchronous design and work at a speed of 475 MHz.
On Code Parameters and Coding Vector Representation for Practical RLNC
DEFF Research Database (Denmark)
Heide, Janus; Pedersen, Morten Videbæk; Fitzek, Frank
2011-01-01
RLNC provides a theoretically efficient method for coding. The drawbacks associated with it are the complexity of the decoding and the overhead resulting from the encoding vector. Increasing the field size and generation size presents a fundamental trade-off between packet-based throughput...... to higher energy consumption. Therefore, the optimal trade-off is system and topology dependent, as it depends on the cost in energy of performing coding operations versus transmitting data. We show that moderate field sizes are the correct choice when trade-offs are considered. The results show that sparse...
Interleaved Product LDPC Codes
Baldi, Marco; Cancellieri, Giovanni; Chiaraluce, Franco
2011-01-01
Product LDPC codes take advantage of LDPC decoding algorithms and the high minimum distance of product codes. We propose to add suitable interleavers to improve the waterfall performance of LDPC decoding. Interleaving also reduces the number of low weight codewords, that gives a further advantage in the error floor region.
Joint Source-Channel Coding by Means of an Oversampled Filter Bank Code
Directory of Open Access Journals (Sweden)
Marinkovic Slavica
2006-01-01
Full Text Available Quantized frame expansions based on block transforms and oversampled filter banks (OFBs have been considered recently as joint source-channel codes (JSCCs for erasure and error-resilient signal transmission over noisy channels. In this paper, we consider a coding chain involving an OFB-based signal decomposition followed by scalar quantization and a variable-length code (VLC or a fixed-length code (FLC. This paper first examines the problem of channel error localization and correction in quantized OFB signal expansions. The error localization problem is treated as an -ary hypothesis testing problem. The likelihood values are derived from the joint pdf of the syndrome vectors under various hypotheses of impulse noise positions, and in a number of consecutive windows of the received samples. The error amplitudes are then estimated by solving the syndrome equations in the least-square sense. The message signal is reconstructed from the corrected received signal by a pseudoinverse receiver. We then improve the error localization procedure by introducing a per-symbol reliability information in the hypothesis testing procedure of the OFB syndrome decoder. The per-symbol reliability information is produced by the soft-input soft-output (SISO VLC/FLC decoders. This leads to the design of an iterative algorithm for joint decoding of an FLC and an OFB code. The performance of the algorithms developed is evaluated in a wavelet-based image coding system.
Performance breakdown in optimal stimulus decoding.
Lubomir Kostal; Lansky, Petr; Pilarski, Stevan
2015-06-01
One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest. In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited. We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision. We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.
From concatenated codes to graph codes
DEFF Research Database (Denmark)
Justesen, Jørn; Høholdt, Tom
2004-01-01
We consider codes based on simple bipartite expander graphs. These codes may be seen as the first step leading from product type concatenated codes to more complex graph codes. We emphasize constructions of specific codes of realistic lengths, and study the details of decoding by message passing...
Considerations and code for partial volume correcting [18F]-AV-1451 tau PET data
Directory of Open Access Journals (Sweden)
Suzanne L. Baker
2017-12-01
Full Text Available [18F]-AV-1451 is a leading tracer used with positron emission tomography (PET to quantify tau pathology. However, [18F]-AV-1451 shows âoff targetâ or non-specific binding, which we define as binding of the tracer in unexpected areas unlikely to harbor aggregated tau based on autopsy literature [1]. Along with caudate, putamen, pallidum and thalamus non-specific binding [2,3], we have found binding in the superior portion of the cerebellar gray matter, leading us to use inferior cerebellar gray as the reference region. We also addressed binding in the posterior portion of the choroid plexus. PET signal unlikely to be associated with tau also occurs in skull, meninges and soft tissue (see e.g. [4]. We refer to [18F]-AV-1451 binding in the skull and meninges as extra-cortical hotspots (ECH and find them near lateral and medial orbitofrontal, lateral occipital, inferior and middle temporal, superior and inferior parietal, and inferior cerebellar gray matter. Lastly, the choroid plexus also shows non-specific binding that bleeds into hippocampus. We are providing the code (http://www.runmycode.org/companion/view/2798 used to create different regions of interest (ROIs that we then used to perform Partial Volume Correction (PVC using the Rousset geometric transfer matrix method (GTM, [5]. This method was used in the companion article, âComparison of multiple tau-PET measures as biomarkers in aging and Alzheimer's Diseaseâ ([6], DOI 10.1016/j.neuroimage.2017.05.058.
Faster 2-regular information-set decoding
Bernstein, D.J.; Lange, T.; Peters, C.P.; Schwabe, P.; Chee, Y.M.
2011-01-01
Fix positive integers B and w. Let C be a linear code over F 2 of length Bw. The 2-regular-decoding problem is to find a nonzero codeword consisting of w length-B blocks, each of which has Hamming weight 0 or 2. This problem appears in attacks on the FSB (fast syndrome-based) hash function and
Fundamentals of convolutional coding
Johannesson, Rolf
2015-01-01
Fundamentals of Convolutional Coding, Second Edition, regarded as a bible of convolutional coding brings you a clear and comprehensive discussion of the basic principles of this field * Two new chapters on low-density parity-check (LDPC) convolutional codes and iterative coding * Viterbi, BCJR, BEAST, list, and sequential decoding of convolutional codes * Distance properties of convolutional codes * Includes a downloadable solutions manual
Design of Packet-Based Block Codes with Shift Operators
Directory of Open Access Journals (Sweden)
Jacek Ilow
2010-01-01
Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of k information packets to construct r redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of k information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of n=k+r received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.
Design of Packet-Based Block Codes with Shift Operators
Directory of Open Access Journals (Sweden)
Ilow Jacek
2010-01-01
Full Text Available This paper introduces packet-oriented block codes for the recovery of lost packets and the correction of an erroneous single packet. Specifically, a family of systematic codes is proposed, based on a Vandermonde matrix applied to a group of information packets to construct redundant packets, where the elements of the Vandermonde matrix are bit-level right arithmetic shift operators. The code design is applicable to packets of any size, provided that the packets within a block of information packets are of uniform length. In order to decrease the overhead associated with packet padding using shift operators, non-Vandermonde matrices are also proposed for designing packet-oriented block codes. An efficient matrix inversion procedure for the off-line design of the decoding algorithm is presented to recover lost packets. The error correction capability of the design is investigated as well. The decoding algorithm, based on syndrome decoding, to correct a single erroneous packet in a group of received packets is presented. The paper is equipped with examples of codes using different parameters. The code designs and their performance are tested using Monte Carlo simulations; the results obtained exhibit good agreement with the corresponding theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Loughry, Thomas A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-02-01
As the volume of data acquired by space-based sensors increases, mission data compression/decompression and forward error correction code processing performance must likewise scale. This competency development effort was explored using the General Purpose Graphics Processing Unit (GPGPU) to accomplish high-rate Rice Decompression and high-rate Reed-Solomon (RS) decoding at the satellite mission ground station. Each algorithm was implemented and benchmarked on a single GPGPU. Distributed processing across one to four GPGPUs was also investigated. The results show that the GPGPU has considerable potential for performing satellite communication Data Signal Processing, with three times or better performance improvements and up to ten times reduction in cost over custom hardware, at least in the case of Rice Decompression and Reed-Solomon Decoding.
International Nuclear Information System (INIS)
Tzika, F.; Stamatelatos, I.E.
2004-01-01
Thermal neutron self-shielding within large samples was studied using the Monte Carlo neutron transport code MCNP. The code enabled a three-dimensional modeling of the actual source and geometry configuration including reactor core, graphite pile and sample. Neutron flux self-shielding correction factors derived for a set of materials of interest for large sample neutron activation analysis are presented and evaluated. Simulations were experimentally verified by measurements performed using activation foils. The results of this study can be applied in order to determine neutron self-shielding factors of unknown samples from the thermal neutron fluxes measured at the surface of the sample
International Nuclear Information System (INIS)
Aoki, Takayuki; Takagi, Toshiyuki
2015-01-01
For creating a corrective measure plan for industrial plant components, it is very important to have a well-grounded basis. Therefore, this paper proposes a method for determining the following three elements of such a plan: an equipment to be repaired, a corrective measure method to be adopted, and a timing of its implementation using a rational approach. And the importance of corrective measure in plant maintenance is also discussed. (author)
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
International Nuclear Information System (INIS)
Kim, Isaac H.
2011-01-01
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
Kim, Isaac H.
2011-05-01
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.
Directory of Open Access Journals (Sweden)
David G. Daut
2007-03-01
Full Text Available A joint source-channel decoding method is designed to accelerate the iterative log-domain sum-product decoding procedure of LDPC codes as well as to improve the reconstructed image quality. Error resilience modes are used in the JPEG2000 source codec making it possible to provide useful source decoded information to the channel decoder. After each iteration, a tentative decoding is made and the channel decoded bits are then sent to the JPEG2000 decoder. The positions of bits belonging to error-free coding passes are then fed back to the channel decoder. The log-likelihood ratios (LLRs of these bits are then modified by a weighting factor for the next iteration. By observing the statistics of the decoding procedure, the weighting factor is designed as a function of the channel condition. Results show that the proposed joint decoding methods can greatly reduce the number of iterations, and thereby reduce the decoding delay considerably. At the same time, this method always outperforms the nonsource controlled decoding method by up to 3 dB in terms of PSNR.
Directory of Open Access Journals (Sweden)
Liu Weiliang
2007-01-01
Full Text Available A joint source-channel decoding method is designed to accelerate the iterative log-domain sum-product decoding procedure of LDPC codes as well as to improve the reconstructed image quality. Error resilience modes are used in the JPEG2000 source codec making it possible to provide useful source decoded information to the channel decoder. After each iteration, a tentative decoding is made and the channel decoded bits are then sent to the JPEG2000 decoder. The positions of bits belonging to error-free coding passes are then fed back to the channel decoder. The log-likelihood ratios (LLRs of these bits are then modified by a weighting factor for the next iteration. By observing the statistics of the decoding procedure, the weighting factor is designed as a function of the channel condition. Results show that the proposed joint decoding methods can greatly reduce the number of iterations, and thereby reduce the decoding delay considerably. At the same time, this method always outperforms the nonsource controlled decoding method by up to 3 dB in terms of PSNR.
Cohen, Aaron M.
2008-01-01
We participated in the i2b2 smoking status classification challenge task. The purpose of this task was to evaluate the ability of systems to automatically identify patient smoking status from discharge summaries. Our submission included several techniques that we compared and studied, including hot-spot identification, zero-vector filtering, inverse class frequency weighting, error-correcting output codes, and post-processing rules. We evaluated our approaches using the same methods as the i2...
1987-01-01
In a television system a digital picture signal is subjected to a transform coding for the purpose of bit rate reduction. In order to detect motion effects between the two fields of a picture, these fields are also examined in a motion detector 8310. If no motion is detected, intraframe transform is
Wall, Candace A.; Rafferty, Lisa A.; Camizzi, Mariya A.; Max, Caroline A.; Van Blargan, David M.
2016-01-01
Many students who struggle to obtain the alphabetic principle are at risk for being identified as having a reading disability and would benefit from additional explicit phonics instruction as a remedial measure. In this action research case study, the research team conducted two experiments to investigate the effects of a color-coded, onset-rime,…
Parallel iterative decoding of transform domain Wyner-Ziv video using cross bitplane correlation
DEFF Research Database (Denmark)
Luong, Huynh Van; Huang, Xin; Forchhammer, Søren
2011-01-01
decoding scheme is proposed to improve the coding efficiency of TDWZ video codecs. The proposed parallel iterative LDPC decoding scheme is able to utilize cross bitplane correlation during decoding, by iteratively refining the soft-input, updating a modeled noise distribution and thereafter enhancing......In recent years, Transform Domain Wyner-Ziv (TDWZ) video coding has been proposed as an efficient Distributed Video Coding (DVC) solution, which fully or partly exploits the source statistics at the decoder to reduce the computational burden at the encoder. In this paper, a parallel iterative LDPC...
DEFF Research Database (Denmark)
Martins, Bo; Forchhammer, Søren
1999-01-01
MPEG-2 video decoding is examined. A unified approach to quality improvement, chrominance upsampling, de-interlacing and superresolution is presented. The information over several frames is combined as part of the processing....
Design of FBG En/decoders in Coherent 2-D Time-polarization OCDMA Systems
Hou, Fen-fei; Yang, Ming
2012-12-01
A novel fiber Bragg grating (FBG)-based en/decoder for the two-dimensional (2-D) time-spreading and polarization multiplexer optical coding is proposed. Compared with other 2-D en/decoders, the proposed en/decoding for an optical code-division multiple-access (OCDMA) system uses a single phase-encoded FBG and coherent en/decoding. Furthermore, combined with reconstruction-equivalent-chirp technology, such en/decoders can be realized with a conventional simple fabrication setup. Experimental results of such en/decoders and the corresponding system test at a data rate of 5 Gbit/s demonstrate that this kind of 2-D FBG-based en/decoders could improve the performances of OCDMA systems.
2002-01-01
Tile Calorimeter modules stored at CERN. The larger modules belong to the Barrel, whereas the smaller ones are for the two Extended Barrels. (The article was about the completion of the 64 modules for one of the latter.) The photo on the first page of the Bulletin n°26/2002, from 24 July 2002, illustrating the article «The ATLAS Tile Calorimeter gets into shape» was published with a wrong caption. We would like to apologise for this mistake and so publish it again with the correct caption.
Using LDPC Code Constraints to Aid Recovery of Symbol Timing
Jones, Christopher; Villasnor, John; Lee, Dong-U; Vales, Esteban
2008-01-01
of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.
Directory of Open Access Journals (Sweden)
2012-01-01
Full Text Available Regarding Gorelik, G., & Shackelford, T.K. (2011. Human sexual conflict from molecules to culture. Evolutionary Psychology, 9, 564–587: The authors wish to correct an omission in citation to the existing literature. In the final paragraph on p. 570, we neglected to cite Burch and Gallup (2006 [Burch, R. L., & Gallup, G. G., Jr. (2006. The psychobiology of human semen. In S. M. Platek & T. K. Shackelford (Eds., Female infidelity and paternal uncertainty (pp. 141–172. New York: Cambridge University Press.]. Burch and Gallup (2006 reviewed the relevant literature on FSH and LH discussed in this paragraph, and should have been cited accordingly. In addition, Burch and Gallup (2006 should have been cited as the originators of the hypothesis regarding the role of FSH and LH in the semen of rapists. The authors apologize for this oversight.
2002-01-01
The photo on the second page of the Bulletin n°48/2002, from 25 November 2002, illustrating the article «Spanish Visit to CERN» was published with a wrong caption. We would like to apologise for this mistake and so publish it again with the correct caption. The Spanish delegation, accompanied by Spanish scientists at CERN, also visited the LHC superconducting magnet test hall (photo). From left to right: Felix Rodriguez Mateos of CERN LHC Division, Josep Piqué i Camps, Spanish Minister of Science and Technology, César Dopazo, Director-General of CIEMAT (Spanish Research Centre for Energy, Environment and Technology), Juan Antonio Rubio, ETT Division Leader at CERN, Manuel Aguilar-Benitez, Spanish Delegate to Council, Manuel Delfino, IT Division Leader at CERN, and Gonzalo León, Secretary-General of Scientific Policy to the Minister.
Directory of Open Access Journals (Sweden)
2014-01-01
Full Text Available Regarding Tagler, M. J., and Jeffers, H. M. (2013. Sex differences in attitudes toward partner infidelity. Evolutionary Psychology, 11, 821–832: The authors wish to correct values in the originally published manuscript. Specifically, incorrect 95% confidence intervals around the Cohen's d values were reported on page 826 of the manuscript where we reported the within-sex simple effects for the significant Participant Sex × Infidelity Type interaction (first paragraph, and for attitudes toward partner infidelity (second paragraph. Corrected values are presented in bold below. The authors would like to thank Dr. Bernard Beins at Ithaca College for bringing these errors to our attention. Men rated sexual infidelity significantly more distressing (M = 4.69, SD = 0.74 than they rated emotional infidelity (M = 4.32, SD = 0.92, F(1, 322 = 23.96, p < .001, d = 0.44, 95% CI [0.23, 0.65], but there was little difference between women's ratings of sexual (M = 4.80, SD = 0.48 and emotional infidelity (M = 4.76, SD = 0.57, F(1, 322 = 0.48, p = .29, d = 0.08, 95% CI [−0.10, 0.26]. As expected, men rated sexual infidelity (M = 1.44, SD = 0.70 more negatively than they rated emotional infidelity (M = 2.66, SD = 1.37, F(1, 322 = 120.00, p < .001, d = 1.12, 95% CI [0.85, 1.39]. Although women also rated sexual infidelity (M = 1.40, SD = 0.62 more negatively than they rated emotional infidelity (M = 2.09, SD = 1.10, this difference was not as large and thus in the evolutionary theory supportive direction, F(1, 322 = 72.03, p < .001, d = 0.77, 95% CI [0.60, 0.94].
Simulations of linear and Hamming codes using SageMath
Timur, Tahta D.; Adzkiya, Dieky; Soleha
2018-03-01
Digital data transmission over a noisy channel could distort the message being transmitted. The goal of coding theory is to ensure data integrity, that is, to find out if and where this noise has distorted the message and what the original message was. Data transmission consists of three stages: encoding, transmission, and decoding. Linear and Hamming codes are codes that we discussed in this work, where encoding algorithms are parity check and generator matrix, and decoding algorithms are nearest neighbor and syndrome. We aim to show that we can simulate these processes using SageMath software, which has built-in class of coding theory in general and linear codes in particular. First we consider the message as a binary vector of size k. This message then will be encoded to a vector with size n using given algorithms. And then a noisy channel with particular value of error probability will be created where the transmission will took place. The last task would be decoding, which will correct and revert the received message back to the original message whenever possible, that is, if the number of error occurred is smaller or equal to the correcting radius of the code. In this paper we will use two types of data for simulations, namely vector and text data.
Decoding and finding the minimum distance with Gröbner bases : history and new insights
Bulygin, S.; Pellikaan, G.R.; Woungang, I.; Misra, S.; Misra, S.C.
2010-01-01
In this chapter, we discuss decoding techniques and finding the minimum distance of linear codes with the use of Grobner bases. First, we give a historical overview of decoding cyclic codes via solving systems polynominal equations over finite fields. In particular, we mention papers of Cooper,.
Yang, Jian-Hua; Li, Jun-Hao; Jiang, Shan; Zhou, Hui; Qu, Liang-Hu
2013-01-01
Long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) represent two classes of important non-coding RNAs in eukaryotes. Although these non-coding RNAs have been implicated in organismal development and in various human diseases, surprisingly little is known about their transcriptional regulation. Recent advances in chromatin immunoprecipitation with next-generation DNA sequencing (ChIP-Seq) have provided methods of detecting transcription factor binding sites (TFBSs) with unprecedented sensitivity. In this study, we describe ChIPBase (http://deepbase.sysu.edu.cn/chipbase/), a novel database that we have developed to facilitate the comprehensive annotation and discovery of transcription factor binding maps and transcriptional regulatory relationships of lncRNAs and miRNAs from ChIP-Seq data. The current release of ChIPBase includes high-throughput sequencing data that were generated by 543 ChIP-Seq experiments in diverse tissues and cell lines from six organisms. By analysing millions of TFBSs, we identified tens of thousands of TF-lncRNA and TF-miRNA regulatory relationships. Furthermore, two web-based servers were developed to annotate and discover transcriptional regulatory relationships of lncRNAs and miRNAs from ChIP-Seq data. In addition, we developed two genome browsers, deepView and genomeView, to provide integrated views of multidimensional data. Moreover, our web implementation supports diverse query types and the exploration of TFs, lncRNAs, miRNAs, gene ontologies and pathways.
A good performance watermarking LDPC code used in high-speed optical fiber communication system
Zhang, Wenbo; Li, Chao; Zhang, Xiaoguang; Xi, Lixia; Tang, Xianfeng; He, Wenxue
2015-07-01
A watermarking LDPC code, which is a strategy designed to improve the performance of the traditional LDPC code, was introduced. By inserting some pre-defined watermarking bits into original LDPC code, we can obtain a more correct estimation about the noise level in the fiber channel. Then we use them to modify the probability distribution function (PDF) used in the initial process of belief propagation (BP) decoding algorithm. This algorithm was tested in a 128 Gb/s PDM-DQPSK optical communication system and results showed that the watermarking LDPC code had a better tolerances to polarization mode dispersion (PMD) and nonlinearity than that of traditional LDPC code. Also, by losing about 2.4% of redundancy for watermarking bits, the decoding efficiency of the watermarking LDPC code is about twice of the traditional one.
Forward Error Correcting Codes for 100 Gbit/s Optical Communication Systems
DEFF Research Database (Denmark)
Li, Bomin
, a denser WDM grid changes the shape of the BER curve based on the analysis of the experimental results, which requires a stronger FEC code. Furthermore, a proof-of-the-concept hardware implementation is presented. The tradeoff between the code length, the CG and the complexity requires more consideration......-complexity low-power-consumption FEC hardware implementation plays an important role in the next generation energy efficient networks. Thirdly, a joint research is required for FEC integrated applications as the error distribution in channels relies on many factors such as non-linearity in long distance optical...... and their associated experimental demonstration and hardware implementation. The demonstrated high CG, flexibility, robustness and scalability reveal the important role of FEC techniques in the next generation high-speed, high-capacity, high performance and energy-efficient fiber-optic data transmission networks....
International Nuclear Information System (INIS)
Johnson, Sarah J; Ong, Lawrence; Shirvanimoghaddam, Mahyar; Lance, Andrew M; Symul, Thomas; Ralph, T C
2017-01-01
The maximum operational range of continuous variable quantum key distribution protocols has shown to be improved by employing high-efficiency forward error correction codes. Typically, the secret key rate model for such protocols is modified to account for the non-zero word error rate of such codes. In this paper, we demonstrate that this model is incorrect: firstly, we show by example that fixed-rate error correction codes, as currently defined, can exhibit efficiencies greater than unity. Secondly, we show that using this secret key model combined with greater than unity efficiency codes, implies that it is possible to achieve a positive secret key over an entanglement breaking channel—an impossible scenario. We then consider the secret key model from a post-selection perspective, and examine the implications for key rate if we constrain the forward error correction codes to operate at low word error rates. (paper)
DEFF Research Database (Denmark)
Lange, Jeppe; Pedersen, Alma B; Troelsen, Anders
2015-01-01
PURPOSE: Administrative discharge registers could be a valuable and easily accessible single-sources for research data on periprosthetic hip joint infection. The aim of this study was to estimate the positive predictive value of the International Classification of Disease 10th revision (ICD-10...... in future single-source register based studies, but preferably should be used in combination with alternate data sources to ensure higher validity....... decreased to 82% (95% CI: 72-89). CONCLUSIONS: Misclassification must be expected and taken into consideration when using administrative discharge registers for epidemiological research on periprosthetic hip joint infection. We believe that the periprosthetic hip joint infection diagnosis code can be of use...
Cohen, Aaron M
2008-01-01
We participated in the i2b2 smoking status classification challenge task. The purpose of this task was to evaluate the ability of systems to automatically identify patient smoking status from discharge summaries. Our submission included several techniques that we compared and studied, including hot-spot identification, zero-vector filtering, inverse class frequency weighting, error-correcting output codes, and post-processing rules. We evaluated our approaches using the same methods as the i2b2 task organizers, using micro- and macro-averaged F1 as the primary performance metric. Our best performing system achieved a micro-F1 of 0.9000 on the test collection, equivalent to the best performing system submitted to the i2b2 challenge. Hot-spot identification, zero-vector filtering, classifier weighting, and error correcting output coding contributed additively to increased performance, with hot-spot identification having by far the largest positive effect. High performance on automatic identification of patient smoking status from discharge summaries is achievable with the efficient and straightforward machine learning techniques studied here.
Pseudo real-time coded aperture imaging system with intensified vidicon cameras
International Nuclear Information System (INIS)
Han, K.S.; Berzins, G.J.
1977-01-01
A coded image displayed on a TV monitor was used to directly reconstruct a decoded image. Both the coded and the decoded images were viewed with intensified vidicon cameras. The coded aperture was a 15-element nonredundant pinhole array. The coding and decoding were accomplished simultaneously during the scanning of a single 16-msec TV frame
Darazi, R.; Gouze, A.; Macq, B.
2009-01-01
Reproducing a natural and real scene as we see in the real world everyday is becoming more and more popular. Stereoscopic and multi-view techniques are used for this end. However due to the fact that more information are displayed requires supporting technologies such as digital compression to ensure the storage and transmission of the sequences. In this paper, a new scheme for stereo image coding is proposed. The original left and right images are jointly coded. The main idea is to optimally exploit the existing correlation between the two images. This is done by the design of an efficient transform that reduces the existing redundancy in the stereo image pair. This approach was inspired by Lifting Scheme (LS). The novelty in our work is that the prediction step is been replaced by an hybrid step that consists in disparity compensation followed by luminance correction and an optimized prediction step. The proposed scheme can be used for lossless and for lossy coding. Experimental results show improvement in terms of performance and complexity compared to recently proposed methods.
Evaluation of Agency Non-Code Layered Pressure Vessels (LPVs). Corrected Copy, Aug. 25, 2014
Prosser, William H.
2014-01-01
In coordination with the Office of Safety and Mission Assurance and the respective Center Pressure System Managers (PSMs), the NASA Engineering and Safety Center (NESC) was requested to formulate a consensus draft proposal for the development of additional testing and analysis methods to establish the technical validity, and any limitation thereof, for the continued safe operation of facility non-code layered pressure vessels. The PSMs from each NASA Center were asked to participate as part of the assessment team by providing, collecting, and reviewing data regarding current operations of these vessels. This report contains the outcome of the assessment and the findings, observations, and NESC recommendations to the Agency and individual NASA Centers.
Rice, Bart F.; Wilde, Carroll O.
It is noted that with the prominence of computers in today's technological society, digital communication systems have become widely used in a variety of applications. Some of the problems that arise in digital communications systems are described. This unit presents the problem of correcting errors in such systems. Error correcting codes are…
Error correcting code with chip kill capability and power saving enhancement
Energy Technology Data Exchange (ETDEWEB)
Gara, Alan G [Mount Kisco, NY; Chen, Dong [Croton On Husdon, NY; Coteus, Paul W [Yorktown Heights, NY; Flynn, William T [Rochester, MN; Marcella, James A [Rochester, MN; Takken, Todd [Brewster, NY; Trager, Barry M [Yorktown Heights, NY; Winograd, Shmuel [Scarsdale, NY
2011-08-30
A method and system are disclosed for detecting memory chip failure in a computer memory system. The method comprises the steps of accessing user data from a set of user data chips, and testing the user data for errors using data from a set of system data chips. This testing is done by generating a sequence of check symbols from the user data, grouping the user data into a sequence of data symbols, and computing a specified sequence of syndromes. If all the syndromes are zero, the user data has no errors. If one of the syndromes is non-zero, then a set of discriminator expressions are computed, and used to determine whether a single or double symbol error has occurred. In the preferred embodiment, less than two full system data chips are used for testing and correcting the user data.
Capacity-Approaching Superposition Coding for Optical Fiber Links
DEFF Research Database (Denmark)
Estaran Tolosa, Jose Manuel; Zibar, Darko; Tafur Monroy, Idelfonso
2014-01-01
We report on the first experimental demonstration of superposition coded modulation (SCM) for polarization-multiplexed coherent-detection optical fiber links. The proposed coded modulation scheme is combined with phase-shifted bit-to-symbol mapping (PSM) in order to achieve geometric and passive......-SCM) is employed in the framework of bit-interleaved coded modulation with iterative decoding (BICM-ID) for forward error correction. The fiber transmission system is characterized in terms of signal-to-noise ratio for back-to-back case and correlated with simulated results for ideal transmission over additive...... white Gaussian noise channel. Thereafter, successful demodulation and decoding after dispersion-unmanaged transmission over 240-km standard single mode fiber of dual-polarization 6-Gbaud 16-, 32- and 64-ary SCM-PSM is experimentally demonstrated....
Osculating Spaces of Varieties and Linear Network Codes
DEFF Research Database (Denmark)
Hansen, Johan P.
2013-01-01
We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces...... intersects in the same dimension. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The obtained osculating spaces of Veronese varieties are equidistant in the above metric. The parameters of the resulting linear network codes...
Osculating Spaces of Varieties and Linear Network Codes
DEFF Research Database (Denmark)
Hansen, Johan P.
We present a general theory to obtain good linear network codes utilizing the osculating nature of algebraic varieties. In particular, we obtain from the osculating spaces of Veronese varieties explicit families of equideminsional vector spaces, in which any pair of distinct vector spaces...... intersects in the same dimension. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The obtained osculating spaces of Veronese varieties are equidistant in the above metric. The parameters of the resulting linear network codes...
Real-time SHVC software decoding with multi-threaded parallel processing
Gudumasu, Srinivas; He, Yuwen; Ye, Yan; He, Yong; Ryu, Eun-Seok; Dong, Jie; Xiu, Xiaoyu
2014-09-01
This paper proposes a parallel decoding framework for scalable HEVC (SHVC). Various optimization technologies are implemented on the basis of SHVC reference software SHM-2.0 to achieve real-time decoding speed for the two layer spatial scalability configuration. SHVC decoder complexity is analyzed with profiling information. The decoding process at each layer and the up-sampling process are designed in parallel and scheduled by a high level application task manager. Within each layer, multi-threaded decoding is applied to accelerate the layer decoding speed. Entropy decoding, reconstruction, and in-loop processing are pipeline designed with multiple threads based on groups of coding tree units (CTU). A group of CTUs is treated as a processing unit in each pipeline stage to achieve a better trade-off between parallelism and synchronization. Motion compensation, inverse quantization, and inverse transform modules are further optimized with SSE4 SIMD instructions. Simulations on a desktop with an Intel i7 processor 2600 running at 3.4 GHz show that the parallel SHVC software decoder is able to decode 1080p spatial 2x at up to 60 fps (frames per second) and 1080p spatial 1.5x at up to 50 fps for those bitstreams generated with SHVC common test conditions in the JCT-VC standardization group. The decoding performance at various bitrates with different optimization technologies and different numbers of threads are compared in terms of decoding speed and resource usage, including processor and memory.
Interactive QR code beautification with full background image embedding
Lin, Lijian; Wu, Song; Liu, Sijiang; Jiang, Bo
2017-06-01
QR (Quick Response) code is a kind of two dimensional barcode that was first developed in automotive industry. Nowadays, QR code has been widely used in commercial applications like product promotion, mobile payment, product information management, etc. Traditional QR codes in accordance with the international standard are reliable and fast to decode, but are lack of aesthetic appearance to demonstrate visual information to customers. In this work, we present a novel interactive method to generate aesthetic QR code. By given information to be encoded and an image to be decorated as full QR code background, our method accepts interactive user's strokes as hints to remove undesired parts of QR code modules based on the support of QR code error correction mechanism and background color thresholds. Compared to previous approaches, our method follows the intention of the QR code designer, thus can achieve more user pleasant result, while keeping high machine readability.
Huang, Jen-Fa; Meng, Sheng-Hui; Lin, Ying-Chen
2014-11-01
The optical code-division multiple-access (OCDMA) technique is considered a good candidate for providing optical layer security. An enhanced OCDMA network security mechanism with a pseudonoise (PN) random digital signals type of maximal-length sequence (M-sequence) code switching to protect against eavesdropping is presented. Signature codes unique to individual OCDMA-network users are reconfigured according to the register state of the controlling electrical shift registers. Examples of signature reconfiguration following state switching of the controlling shift register for both the network user and the eavesdropper are numerically illustrated. Dynamically changing the PN state of the shift register to reconfigure the user signature sequence is shown; this hinders eavesdroppers' efforts to decode correct data sequences. The proposed scheme increases the probability of eavesdroppers committing errors in decoding and thereby substantially enhances the degree of an OCDMA network's confidentiality.
Wootton, James R.; Loss, Daniel
2018-05-01
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most 15 qubits on the 16 qubit ibmqx3 device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.
Khina, Anatoly
2016-08-15
We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding with an error probability profile that decays exponentially with the decoding delay. The works of Schulman and Sahai over the past two decades have developed the notions of tree codes and anytime capacity, and provided the theoretical framework for studying such problems. Nonetheless, there has been little practical progress in this area due to the absence of explicit constructions of tree codes with efficient encoding and decoding algorithms. Recently, linear time-invariant tree codes were proposed to achieve the desired result under maximum-likelihood decoding. In this work, we take one more step towards practicality, by showing that these codes can be efficiently decoded using sequential decoding algorithms, up to some loss in performance (and with some practical complexity caveats). We supplement our theoretical results with numerical simulations that demonstrate the effectiveness of the decoder in a control system setting.
Constructing LDPC Codes from Loop-Free Encoding Modules
Divsalar, Dariush; Dolinar, Samuel; Jones, Christopher; Thorpe, Jeremy; Andrews, Kenneth
2009-01-01
A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to
Towards self-correcting quantum memories
Michnicki, Kamil
This thesis presents a model of self-correcting quantum memories where quantum states are encoded using topological stabilizer codes and error correction is done using local measurements and local dynamics. Quantum noise poses a practical barrier to developing quantum memories. This thesis explores two types of models for suppressing noise. One model suppresses thermalizing noise energetically by engineering a Hamiltonian with a high energy barrier between code states. Thermalizing dynamics are modeled phenomenologically as a Markovian quantum master equation with only local generators. The second model suppresses stochastic noise with a cellular automaton that performs error correction using syndrome measurements and a local update rule. Several ways of visualizing and thinking about stabilizer codes are presented in order to design ones that have a high energy barrier: the non-local Ising model, the quasi-particle graph and the theory of welded stabilizer codes. I develop the theory of welded stabilizer codes and use it to construct a code with the highest known energy barrier in 3-d for spin Hamiltonians: the welded solid code. Although the welded solid code is not fully self correcting, it has some self correcting properties. It has an increased memory lifetime for an increased system size up to a temperature dependent maximum. One strategy for increasing the energy barrier is by mediating an interaction with an external system. I prove a no-go theorem for a class of Hamiltonians where the interaction terms are local, of bounded strength and commute with the stabilizer group. Under these conditions the energy barrier can only be increased by a multiplicative constant. I develop cellular automaton to do error correction on a state encoded using the toric code. The numerical evidence indicates that while there is no threshold, the model can extend the memory lifetime significantly. While of less theoretical importance, this could be practical for real
DEFF Research Database (Denmark)
Sørensen, Jesper Hemming; Koike-Akino, Toshiaki; Orlik, Philip
2012-01-01
This paper proposes a concept called rateless feedback coding. We redesign the existing LT and Raptor codes, by introducing new degree distributions for the case when a few feedback opportunities are available. We show that incorporating feedback to LT codes can significantly decrease both...... the coding overhead and the encoding/decoding complexity. Moreover, we show that, at the price of a slight increase in the coding overhead, linear complexity is achieved with Raptor feedback coding....
Decoding spikes in a spiking neuronal network
Energy Technology Data Exchange (ETDEWEB)
Feng Jianfeng [Department of Informatics, University of Sussex, Brighton BN1 9QH (United Kingdom); Ding, Mingzhou [Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431 (United States)
2004-06-04
We investigate how to reliably decode the input information from the output of a spiking neuronal network. A maximum likelihood estimator of the input signal, together with its Fisher information, is rigorously calculated. The advantage of the maximum likelihood estimation over the 'brute-force rate coding' estimate is clearly demonstrated. It is pointed out that the ergodic assumption in neuroscience, i.e. a temporal average is equivalent to an ensemble average, is in general not true. Averaging over an ensemble of neurons usually gives a biased estimate of the input information. A method on how to compensate for the bias is proposed. Reconstruction of dynamical input signals with a group of spiking neurons is extensively studied and our results show that less than a spike is sufficient to accurately decode dynamical inputs.
Decoding spikes in a spiking neuronal network
International Nuclear Information System (INIS)
Feng Jianfeng; Ding, Mingzhou
2004-01-01
We investigate how to reliably decode the input information from the output of a spiking neuronal network. A maximum likelihood estimator of the input signal, together with its Fisher information, is rigorously calculated. The advantage of the maximum likelihood estimation over the 'brute-force rate coding' estimate is clearly demonstrated. It is pointed out that the ergodic assumption in neuroscience, i.e. a temporal average is equivalent to an ensemble average, is in general not true. Averaging over an ensemble of neurons usually gives a biased estimate of the input information. A method on how to compensate for the bias is proposed. Reconstruction of dynamical input signals with a group of spiking neurons is extensively studied and our results show that less than a spike is sufficient to accurately decode dynamical inputs
CERN. Geneva. Audiovisual Unit; Antonerakis, S E
2002-01-01
Decoding the Human genome is a very up-to-date topic, raising several questions besides purely scientific, in view of the two competing teams (public and private), the ethics of using the results, and the fact that the project went apparently faster and easier than expected. The lecture series will address the following chapters: Scientific basis and challenges. Ethical and social aspects of genomics.
International Nuclear Information System (INIS)
Barreras Caballero, A. A.; Hernandez Garcia, J.J.; Alfonso Laguardia, R.
2009-01-01
Were directly determined correction factors depending on the type camera beam quality, k, Q, and kQ, Qo, instead of the product (w, air p) Q, for three type cylindrical ionization chambers Pinpoint and divergent monoenergetic beams of photons in a wide range of energies (4-20 MV). The method of calculation used dispenses with the approaches taken in the classic procedure considered independent of braking power ratios and the factors disturbance of the camera. A detailed description of the geometry and materials chambers were supplied by the manufacturer and used as data input for the system 2006 of PENELOPE Monte Carlo calculation using a User code that includes correlated sampling, and forced interactions division of particles. We used a photon beam Co-60 as beam reference for calculating the correction factors for beam quality. No data exist for the cameras PTW 31014, 31015 and 31016 in the TRS-398 at they do not compare the results with data calculated or determined experimentally by other authors. (author)
A Fully Parallel VLSI-implementation of the Viterbi Decoding Algorithm
DEFF Research Database (Denmark)
Sparsø, Jens; Jørgensen, Henrik Nordtorp; Paaske, Erik
1989-01-01
In this paper we describe the implementation of a K = 7, R = 1/2 single-chip Viterbi decoder intended to operate at 10-20 Mbit/sec. We propose a general, regular and area efficient floor-plan that is also suitable for implementation of decoders for codes with different generator polynomials...
Cascading Oscillators in Decoding Speech: Reflection of a Cortical Computation Principle
2016-09-06
purely) auditory or articulatory model can explain this behavior. The insertion of gaps was interpreted as the act of providing extra decoding time...The windows are generated by a segmentation process, implemented by an array of cascaded oscillators. Correct segmentation is a critical...prerequisite for correct decoding, and segmentation is correct as long as the oscillators successfully track the input rhythms. Syllabic segmentation utilizes
Error-correcting pairs for a public-key cryptosystem
International Nuclear Information System (INIS)
Pellikaan, Ruud; Márquez-Corbella, Irene
2017-01-01
Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification. The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken. One of the main requirements of a code-based cryptosystem is having high performance t -bounded decoding algorithms which is achieved in the case the code has a t -error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair. In this paper, the class of codes with a t -ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t -error correcting pair. (paper)
A new LDPC decoding scheme for PDM-8QAM BICM coherent optical communication system
Liu, Yi; Zhang, Wen-bo; Xi, Li-xia; Tang, Xian-feng; Zhang, Xiao-guang
2015-11-01
A new log-likelihood ratio (LLR) message estimation method is proposed for polarization-division multiplexing eight quadrature amplitude modulation (PDM-8QAM) bit-interleaved coded modulation (BICM) optical communication system. The formulation of the posterior probability is theoretically analyzed, and the way to reduce the pre-decoding bit error rate ( BER) of the low density parity check (LDPC) decoder for PDM-8QAM constellations is presented. Simulation results show that it outperforms the traditional scheme, i.e., the new post-decoding BER is decreased down to 50% of that of the traditional post-decoding algorithm.
Feature reconstruction of LFP signals based on PLSR in the neural information decoding study.
Yonghui Dong; Zhigang Shang; Mengmeng Li; Xinyu Liu; Hong Wan
2017-07-01
To solve the problems of Signal-to-Noise Ratio (SNR) and multicollinearity when the Local Field Potential (LFP) signals is used for the decoding of animal motion intention, a feature reconstruction of LFP signals based on partial least squares regression (PLSR) in the neural information decoding study is proposed in this paper. Firstly, the feature information of LFP coding band is extracted based on wavelet transform. Then the PLSR model is constructed by the extracted LFP coding features. According to the multicollinearity characteristics among the coding features, several latent variables which contribute greatly to the steering behavior are obtained, and the new LFP coding features are reconstructed. Finally, the K-Nearest Neighbor (KNN) method is used to classify the reconstructed coding features to verify the decoding performance. The results show that the proposed method can achieve the highest accuracy compared to the other three methods and the decoding effect of the proposed method is robust.
Entanglement-assisted quantum low-density parity-check codes
International Nuclear Information System (INIS)
Fujiwara, Yuichiro; Clark, David; Tonchev, Vladimir D.; Vandendriessche, Peter; De Boeck, Maarten
2010-01-01
This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error-correction performance, high rates, and low decoding complexity. The proposed method produces several infinite families of codes with a wide variety of parameters and entanglement requirements. Our framework encompasses the previously known entanglement-assisted quantum LDPC codes having the best error-correction performance and many other codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.
Performance-complexity tradeoff in sequential decoding for the unconstrained AWGN channel
Abediseid, Walid
2013-06-01
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter - the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity. © 2013 IEEE.
Unitals and ovals of symmetric block designs in LDPC and space-time coding
Andriamanalimanana, Bruno R.
2004-08-01
An approach to the design of LDPC (low density parity check) error-correction and space-time modulation codes involves starting with known mathematical and combinatorial structures, and deriving code properties from structure properties. This paper reports on an investigation of unital and oval configurations within generic symmetric combinatorial designs, not just classical projective planes, as the underlying structure for classes of space-time LDPC outer codes. Of particular interest are the encoding and iterative (sum-product) decoding gains that these codes may provide. Various small-length cases have been numerically implemented in Java and Matlab for a number of channel models.
LDPC-PPM Coding Scheme for Optical Communication
Barsoum, Maged; Moision, Bruce; Divsalar, Dariush; Fitz, Michael
2009-01-01
In a proposed coding-and-modulation/demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes. Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (a^) of the coded data, which is then processed by a decoder to obtain an estimate (u^) of the original data.
An efficient chaotic source coding scheme with variable-length blocks
International Nuclear Information System (INIS)
Lin Qiu-Zhen; Wong Kwok-Wo; Chen Jian-Yong
2011-01-01
An efficient chaotic source coding scheme operating on variable-length blocks is proposed. With the source message represented by a trajectory in the state space of a chaotic system, data compression is achieved when the dynamical system is adapted to the probability distribution of the source symbols. For infinite-precision computation, the theoretical compression performance of this chaotic coding approach attains that of optimal entropy coding. In finite-precision implementation, it can be realized by encoding variable-length blocks using a piecewise linear chaotic map within the precision of register length. In the decoding process, the bit shift in the register can track the synchronization of the initial value and the corresponding block. Therefore, all the variable-length blocks are decoded correctly. Simulation results show that the proposed scheme performs well with high efficiency and minor compression loss when compared with traditional entropy coding. (general)
Analysis of Minimal LDPC Decoder System on a Chip Implementation
Directory of Open Access Journals (Sweden)
T. Palenik
2015-09-01
Full Text Available This paper presents a practical method of potential replacement of several different Quasi-Cyclic Low-Density Parity-Check (QC-LDPC codes with one, with the intention of saving as much memory as required to implement the LDPC encoder and decoder in a memory-constrained System on a Chip (SoC. The presented method requires only a very small modification of the existing encoder and decoder, making it suitable for utilization in a Software Defined Radio (SDR platform. Besides the analysis of the effects of necessary variable-node value fixation during the Belief Propagation (BP decoding algorithm, practical standard-defined code parameters are scrutinized in order to evaluate the feasibility of the proposed LDPC setup simplification. Finally, the error performance of the modified system structure is evaluated and compared with the original system structure by means of simulation.
Decoding Facial Expressions: A New Test with Decoding Norms.
Leathers, Dale G.; Emigh, Ted H.
1980-01-01
Describes the development and testing of a new facial meaning sensitivity test designed to determine how specialized are the meanings that can be decoded from facial expressions. Demonstrates the use of the test to measure a receiver's current level of skill in decoding facial expressions. (JMF)
Rate-adaptive BCH codes for distributed source coding
DEFF Research Database (Denmark)
Salmistraro, Matteo; Larsen, Knud J.; Forchhammer, Søren
2013-01-01
This paper considers Bose-Chaudhuri-Hocquenghem (BCH) codes for distributed source coding. A feedback channel is employed to adapt the rate of the code during the decoding process. The focus is on codes with short block lengths for independently coding a binary source X and decoding it given its...... strategies for improving the reliability of the decoded result are analyzed, and methods for estimating the performance are proposed. In the analysis, noiseless feedback and noiseless communication are assumed. Simulation results show that rate-adaptive BCH codes achieve better performance than low...... correlated side information Y. The proposed codes have been analyzed in a high-correlation scenario, where the marginal probability of each symbol, Xi in X, given Y is highly skewed (unbalanced). Rate-adaptive BCH codes are presented and applied to distributed source coding. Adaptive and fixed checking...
Logical error rate scaling of the toric code
International Nuclear Information System (INIS)
Watson, Fern H E; Barrett, Sean D
2014-01-01
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical quantum computers will necessarily operate below these thresholds meaning that other performance indicators become important. In this work we consider the scaling of the logical error rate of the toric code and demonstrate how, in turn, this may be used to calculate a key performance indicator. We use a perfect matching decoding algorithm to find the scaling of the logical error rate and find two distinct operating regimes. The first regime admits a universal scaling analysis due to a mapping to a statistical physics model. The second regime characterizes the behaviour in the limit of small physical error rate and can be understood by counting the error configurations leading to the failure of the decoder. We present a conjecture for the ranges of validity of these two regimes and use them to quantify the overhead—the total number of physical qubits required to perform error correction. (paper)
Analysis of error-correction constraints in an optical disk
Roberts, Jonathan D.; Ryley, Alan; Jones, David M.; Burke, David
1996-07-01
The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.
3D Measurement Technology by Structured Light Using Stripe-Edge-Based Gray Code
International Nuclear Information System (INIS)
Wu, H B; Chen, Y; Wu, M Y; Guan, C R; Yu, X Y
2006-01-01
The key problem of 3D vision measurement using triangle method based on structured light is to acquiring projecting angle of projecting light accurately. In order to acquire projecting angle thereby determine the corresponding relationship between sampling point and image point, method for encoding and decoding structured light based on stripe edge of Gray code is presented. The method encoded with Gray code stripe and decoded with stripe edge acquired by sub-pixel technology instead of pixel centre, so latter one-bit decoding error was removed. Accuracy of image sampling point location and correspondence between image sampling point and object sampling point achieved sub-pixel degree. In addition, measurement error caused by dividing projecting angle irregularly by even-width encoding stripe was analysed and corrected. Encoding and decoding principle and decoding equations were described. Finally, 3dsmax and Matlab software were used to simulate measurement system and reconstruct measured surface. Indicated by experimental results, measurement error is about 0.05%
International Nuclear Information System (INIS)
Mazurier, J.
1999-01-01
This thesis has been performed in the framework of national reference setting-up for absorbed dose in water and high energy photon beam provided with the SATURNE-43 medical accelerator of the BNM-LPRI (acronym for National Bureau of Metrology and Primary standard laboratory of ionising radiation). The aim of this work has been to develop and validate different user codes, based on PENELOPE Monte Carlo code system, to determine the photon beam characteristics and calculate the correction factors of reference dosimeters such as Fricke dosimeters and graphite calorimeter. In the first step, the developed user codes have permitted the influence study of different components constituting the irradiation head. Variance reduction techniques have been used to reduce the calculation time. The phase space has been calculated for 6, 12 and 25 MV at the output surface level of the accelerator head, then used for calculating energy spectra and dose distributions in the reference water phantom. Results obtained have been compared with experimental measurements. The second step has been devoted to develop an user code allowing calculation correction factors associated with both BNM-LPRI's graphite and Fricke dosimeters thanks to a correlated sampling method starting with energy spectra obtained in the first step. Then the calculated correction factors have been compared with experimental and calculated results obtained with the Monte Carlo EGS4 code system. The good agreement, between experimental and calculated results, leads to validate simulations performed with the PENELOPE code system. (author)
Rajagopalan, Kanavillil
2006-01-01
The objective of this response article is to think through some of what I see as the far-reaching implications of a recent paper by Eric Hauser (2005) entitled "Coding 'corrective recasts': the maintenance of meaning and more fundamental problems". Hauser makes a compelling, empirically-backed case for his contention that, contrary to widespread…
Directory of Open Access Journals (Sweden)
Gou Hosoya
2013-01-01
Full Text Available Approximate calculation of channel log-likelihood ratio (LLR for wireless channels using Padé approximation is presented. LLR is used as an input of iterative decoding for powerful error-correcting codes such as low-density parity-check (LDPC codes or turbo codes. Due to the lack of knowledge of the channel state information of a wireless fading channel, such as uncorrelated fiat Rayleigh fading channels, calculations of exact LLR for these channels are quite complicated for a practical implementation. The previous work, an LLR calculation using the Taylor approximation, quickly becomes inaccurate as the channel output leaves some derivative point. This becomes a big problem when higher order modulation scheme is employed. To overcome this problem, a new LLR approximation using Padé approximation, which expresses the original function by a rational form of two polynomials with the same total number of coefficients of the Taylor series and can accelerate the Taylor approximation, is devised. By applying the proposed approximation to the iterative decoding and the LDPC codes with some modulation schemes, we show the effectiveness of the proposed methods by simulation results and analysis based on the density evolution.
tRNA's wobble decoding of the genome: 40 years of modification.
Agris, Paul F; Vendeix, Franck A P; Graham, William D
2007-02-09
The genetic code is degenerate, in that 20 amino acids are encoded by 61 triplet codes. In 1966, Francis Crick hypothesized that the cell's limited number of tRNAs decoded the genome by recognizing more than one codon. The ambiguity of that recognition resided in the third base-pair, giving rise to the Wobble Hypothesis. Post-transcriptional modifications at tRNA's wobble position 34, especially modifications of uridine 34, enable wobble to occur. The Modified Wobble Hypothesis proposed in 1991 that specific modifications of a tRNA wobble nucleoside shape the anticodon architecture in such a manner that interactions were restricted to the complementary base plus a single wobble pairing for amino acids with twofold degenerate codons. However, chemically different modifications at position 34 would expand the ability of a tRNA to read three or even four of the fourfold degenerate codons. One foundation of Crick's Wobble Hypothesis was that a near-constant geometry of canonical base-pairing be maintained in forming all three base-pairs between the tRNA anticodon and mRNA codon on the ribosome. In accepting an aminoacyl-tRNA, the ribosome requires maintenance of a specific geometry for the anticodon-codon base-pairing. However, it is the post-transcriptional modifications at tRNA wobble position 34 and purine 37, 3'-adjacent to the anticodon, that pre-structure the anticodon domain to ensure the correct codon binding. The modifications create both the architecture and the stability needed for decoding through restraints on anticodon stereochemistry and conformational space, and through selective hydrogen bonding. A physicochemical understanding of modified nucleoside contributions to the tRNA anticodon domain architecture and its decoding of the genome has advanced RNA world evolutionary theory, the principles of RNA chemistry, and the application of this knowledge to the introduction of new amino acids to proteins.
International Nuclear Information System (INIS)
Toivonen, Matti.
1979-07-01
One, two and three-component dosemeter cards and their associated processing equipment were developed for personnel monitoring. A novel feature of the TLD system is that the individual sensitivity correction factors of TL detectors for β/γ radiation dosimetry and special timing factors for the readout of neutron detectors are stored on dosemeter cards as an extension of the identity codes. These data are utilized in the automatic TL reading process with the aim of cancelling out the influence of the individual detector characteristics on the measuring results. Stimulation of TL is done with hot nitrogen without removing the detectors from their cards and without any metal contact. Changes in detector characteristics are thus improbable. The reading process can be adjusted in a variety of ways. For example, each detector in the same card can be processed with optimal heating and the specific 250 deg C glow peak of neutron radiation can be roughly separated from the main LiF glow peaks. (author)
Smaller decoding exponents : ball-collision decoding
Bernstein, D.J.; Lange, T.; Peters, C.P.; Rogaway, P.
2011-01-01
Very few public-key cryptosystems are known that can encrypt and decrypt in time $ b^{ 2¿+¿o(1) } $with conjectured security level $2^b$ against conventional computers and quantum computers. The oldest of these systems is the classic McEliece code-based cryptosystem. The best attacks known against
Maximum a posteriori decoder for digital communications
Altes, Richard A. (Inventor)
1997-01-01
A system and method for decoding by identification of the most likely phase coded signal corresponding to received data. The present invention has particular application to communication with signals that experience spurious random phase perturbations. The generalized estimator-correlator uses a maximum a posteriori (MAP) estimator to generate phase estimates for correlation with incoming data samples and for correlation with mean phases indicative of unique hypothesized signals. The result is a MAP likelihood statistic for each hypothesized transmission, wherein the highest value statistic identifies the transmitted signal.
Upper Bounds on the Number of Errors Corrected by the Koetter–Vardy Algorithm
DEFF Research Database (Denmark)
Justesen, Jørn
2007-01-01
By introducing a few simplifying assumptions we derive a simple condition for successful decoding using the Koetter-Vardy algorithm for soft-decision decoding of Reed-Solomon codes. We show that the algorithm has a significant advantage over hard decision decoding when the code rate is low, when ...
Directory of Open Access Journals (Sweden)
Liu Yu-Sun
2011-01-01
Full Text Available Abstract The performance of the wrap-around Viterbi decoding algorithm with finite truncation depth and fixed decoding trellis length is investigated for tail-biting convolutional codes in the mobile WiMAX standard. Upper bounds on the error probabilities induced by finite truncation depth and the uncertainty of the initial state are derived for the AWGN channel. The truncation depth and the decoding trellis length that yield negligible performance loss are obtained for all transmission rates over the Rayleigh channel using computer simulations. The results show that the circular decoding algorithm with an appropriately chosen truncation depth and a decoding trellis just a fraction longer than the original received code words can achieve almost the same performance as the optimal maximum likelihood decoding algorithm in mobile WiMAX. A rule of thumb for the values of the truncation depth and the trellis tail length is also proposed.
Cellular automaton decoders of topological quantum memories in the fault tolerant setting
International Nuclear Information System (INIS)
Herold, Michael; Eisert, Jens; Kastoryano, Michael J; Campbell, Earl T
2017-01-01
Active error decoding and correction of topological quantum codes—in particular the toric code—remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder. (paper)
Coded Splitting Tree Protocols
DEFF Research Database (Denmark)
Sørensen, Jesper Hemming; Stefanovic, Cedomir; Popovski, Petar
2013-01-01
This paper presents a novel approach to multiple access control called coded splitting tree protocol. The approach builds on the known tree splitting protocols, code structure and successive interference cancellation (SIC). Several instances of the tree splitting protocol are initiated, each...... instance is terminated prematurely and subsequently iterated. The combined set of leaves from all the tree instances can then be viewed as a graph code, which is decodable using belief propagation. The main design problem is determining the order of splitting, which enables successful decoding as early...
Bogler, Carsten; Mehnert, Jan; Steinbrink, Jens; Haynes, John-Dylan
2014-01-01
Sustained, long-term cognitive workload is associated with variations and decrements in performance. Such fluctuations in vigilance can be a risk factor especially during dangerous attention demanding activities. Functional MRI studies have shown that attentional performance is correlated with BOLD-signals, especially in parietal and prefrontal cortical regions. An interesting question is whether these BOLD-signals could be measured in real-world scenarios, say to warn in a dangerous workplace whenever a subjects' vigilance is low. Because fMRI lacks the mobility needed for such applications, we tested whether the monitoring of vigilance might be possible using Near-Infrared Spectroscopy (NIRS). NIRS is a highly mobile technique that measures hemodynamics in the surface of the brain. We demonstrate that non-invasive NIRS signals correlate with vigilance. These signals carry enough information to decode subjects' reaction times at a single trial level.
Directory of Open Access Journals (Sweden)
Carsten Bogler
Full Text Available Sustained, long-term cognitive workload is associated with variations and decrements in performance. Such fluctuations in vigilance can be a risk factor especially during dangerous attention demanding activities. Functional MRI studies have shown that attentional performance is correlated with BOLD-signals, especially in parietal and prefrontal cortical regions. An interesting question is whether these BOLD-signals could be measured in real-world scenarios, say to warn in a dangerous workplace whenever a subjects' vigilance is low. Because fMRI lacks the mobility needed for such applications, we tested whether the monitoring of vigilance might be possible using Near-Infrared Spectroscopy (NIRS. NIRS is a highly mobile technique that measures hemodynamics in the surface of the brain. We demonstrate that non-invasive NIRS signals correlate with vigilance. These signals carry enough information to decode subjects' reaction times at a single trial level.
Astrophysics Decoding the cosmos
Irwin, Judith A
2007-01-01
Astrophysics: Decoding the Cosmos is an accessible introduction to the key principles and theories underlying astrophysics. This text takes a close look at the radiation and particles that we receive from astronomical objects, providing a thorough understanding of what this tells us, drawing the information together using examples to illustrate the process of astrophysics. Chapters dedicated to objects showing complex processes are written in an accessible manner and pull relevant background information together to put the subject firmly into context. The intention of the author is that the book will be a 'tool chest' for undergraduate astronomers wanting to know the how of astrophysics. Students will gain a thorough grasp of the key principles, ensuring that this often-difficult subject becomes more accessible.
A graph model for opportunistic network coding
Sorour, Sameh; Aboutoraby, Neda; Al-Naffouri, Tareq Y.; Alouini, Mohamed-Slim
2015-01-01
© 2015 IEEE. Recent advancements in graph-based analysis and solutions of instantly decodable network coding (IDNC) trigger the interest to extend them to more complicated opportunistic network coding (ONC) scenarios, with limited increase
High-throughput GPU-based LDPC decoding
Chang, Yang-Lang; Chang, Cheng-Chun; Huang, Min-Yu; Huang, Bormin
2010-08-01
Low-density parity-check (LDPC) code is a linear block code known to approach the Shannon limit via the iterative sum-product algorithm. LDPC codes have been adopted in most current communication systems such as DVB-S2, WiMAX, WI-FI and 10GBASE-T. LDPC for the needs of reliable and flexible communication links for a wide variety of communication standards and configurations have inspired the demand for high-performance and flexibility computing. Accordingly, finding a fast and reconfigurable developing platform for designing the high-throughput LDPC decoder has become important especially for rapidly changing communication standards and configurations. In this paper, a new graphic-processing-unit (GPU) LDPC decoding platform with the asynchronous data transfer is proposed to realize this practical implementation. Experimental results showed that the proposed GPU-based decoder achieved 271x speedup compared to its CPU-based counterpart. It can serve as a high-throughput LDPC decoder.
Concurrent Codes: A Holographic-Type Encoding Robust against Noise and Loss.
Directory of Open Access Journals (Sweden)
David M Benton
Full Text Available Concurrent coding is an encoding scheme with 'holographic' type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst errors simultaneously, but does not rely on cyclic codes. A simple and practical scheme has been tested that displays perfect decoding when the signal to noise ratio is of order -18dB. The same scheme also displays perfect reconstruction when a contiguous block of 40% of the transmission is missing. In addition this scheme is 50% more efficient in terms of transmitted power requirements than equivalent cyclic codes. A simple model is presented that describes the process of decoding and can determine the computational load that would be expected, as well as describing the critical levels of noise and missing data at which false messages begin to be generated.
Ni, Jianjun David
2011-01-01
This presentation briefly discusses a research effort on mitigation techniques of pulsed radio frequency interference (RFI) on a Low-Density-Parity-Check (LDPC) code. This problem is of considerable interest in the context of providing reliable communications to the space vehicle which might suffer severe degradation due to pulsed RFI sources such as large radars. The LDPC code is one of modern forward-error-correction (FEC) codes which have the decoding performance to approach the Shannon Limit. The LDPC code studied here is the AR4JA (2048, 1024) code recommended by the Consultative Committee for Space Data Systems (CCSDS) and it has been chosen for some spacecraft design. Even though this code is designed as a powerful FEC code in the additive white Gaussian noise channel, simulation data and test results show that the performance of this LDPC decoder is severely degraded when exposed to the pulsed RFI specified in the spacecraft s transponder specifications. An analysis work (through modeling and simulation) has been conducted to evaluate the impact of the pulsed RFI and a few implemental techniques have been investigated to mitigate the pulsed RFI impact by reshuffling the soft-decision-data available at the input of the LDPC decoder. The simulation results show that the LDPC decoding performance of codeword error rate (CWER) under pulsed RFI can be improved up to four orders of magnitude through a simple soft-decision-data reshuffle scheme. This study reveals that an error floor of LDPC decoding performance appears around CWER=1E-4 when the proposed technique is applied to mitigate the pulsed RFI impact. The mechanism causing this error floor remains unknown, further investigation is necessary.
Complexity Analysis of Reed-Solomon Decoding over GF(2m without Using Syndromes
Directory of Open Access Journals (Sweden)
Zhiyuan Yan
2008-06-01
Full Text Available There has been renewed interest in decoding Reed-Solomon (RS codes without using syndromes recently. In this paper, we investigate the complexity of syndromeless decoding, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis focuses on RS codes over characteristic-2 fields, for which some multiplicative FFT techniques are not applicable. Due to moderate block lengths of RS codes in practice, our analysis is complete, without big O notation. In addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. For high-rate RS codes, when compared to syndrome-based decoding algorithms, not only syndromeless decoding algorithms require more field operations regardless of implementation, but also decoder architectures based on their direct implementations have higher hardware costs and lower throughput. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.
Complexity Analysis of Reed-Solomon Decoding over GF without Using Syndromes
Directory of Open Access Journals (Sweden)
Chen Ning
2008-01-01
Full Text Available Abstract There has been renewed interest in decoding Reed-Solomon (RS codes without using syndromes recently. In this paper, we investigate the complexity of syndromeless decoding, and compare it to that of syndrome-based decoding. Aiming to provide guidelines to practical applications, our complexity analysis focuses on RS codes over characteristic-2 fields, for which some multiplicative FFT techniques are not applicable. Due to moderate block lengths of RS codes in practice, our analysis is complete, without big notation. In addition to fast implementation using additive FFT techniques, we also consider direct implementation, which is still relevant for RS codes with moderate lengths. For high-rate RS codes, when compared to syndrome-based decoding algorithms, not only syndromeless decoding algorithms require more field operations regardless of implementation, but also decoder architectures based on their direct implementations have higher hardware costs and lower throughput. We also derive tighter bounds on the complexities of fast polynomial multiplications based on Cantor's approach and the fast extended Euclidean algorithm.
Modeling coherent errors in quantum error correction
Greenbaum, Daniel; Dutton, Zachary
2018-01-01
Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Pauli model. Here we examine the accuracy of the Pauli approximation for noise containing coherent errors (characterized by a rotation angle ɛ) under the repetition code. We derive an analytic expression for the logical error channel as a function of arbitrary code distance d and concatenation level n, in the small error limit. We find that coherent physical errors result in logical errors that are partially coherent and therefore non-Pauli. However, the coherent part of the logical error is negligible at fewer than {ε }-({dn-1)} error correction cycles when the decoder is optimized for independent Pauli errors, thus providing a regime of validity for the Pauli approximation. Above this number of correction cycles, the persistent coherent logical error will cause logical failure more quickly than the Pauli model would predict, and this may need to be combated with coherent suppression methods at the physical level or larger codes.
LDGM Codes for Channel Coding and Joint Source-Channel Coding of Correlated Sources
Directory of Open Access Journals (Sweden)
Javier Garcia-Frias
2005-05-01
Full Text Available We propose a coding scheme based on the use of systematic linear codes with low-density generator matrix (LDGM codes for channel coding and joint source-channel coding of multiterminal correlated binary sources. In both cases, the structures of the LDGM encoder and decoder are shown, and a concatenated scheme aimed at reducing the error floor is proposed. Several decoding possibilities are investigated, compared, and evaluated. For different types of noisy channels and correlation models, the resulting performance is very close to the theoretical limits.
Rate-Compatible Protograph LDPC Codes
Nguyen, Thuy V. (Inventor); Nosratinia, Aria (Inventor); Divsalar, Dariush (Inventor)
2014-01-01
Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.
Muhammad Asif; H.M.Rehan Afzal
2015-01-01
Convolutional codes are also known as Turbo codes because of their error correction capability. These codes are also awarded as Super product codes, because these codes have replaced the backward error correction codes. Turbo codes are much more efficient than previous backward error correction codes because these are Forward error correction (FEC) codes and there is no need for a feedback link to request the transmitter for retransmission of data, when bits are corrupted in the i...
A novel QC-LDPC code based on the finite field multiplicative group for optical communications
Yuan, Jian-guo; Xu, Liang; Tong, Qing-zhen
2013-09-01
A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) code is proposed based on the finite field multiplicative group, which has easier construction, more flexible code-length code-rate adjustment and lower encoding/decoding complexity. Moreover, a regular QC-LDPC(5334,4962) code is constructed. The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise (AWGN) channel with iterative decoding sum-product algorithm (SPA). At the bit error rate (BER) of 10-6, the net coding gain (NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB, 0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975, the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method, respectively. So it is more suitable for optical communication systems.
Shi, Zhiping; Yan, Bing
2010-08-01
In multiple-input multiple-output(MIMO) wireless systems, combining good channel codes(e.g., Non-binary Repeat Accumulate codes) with adaptive turbo equalization is a good option to get better performance and lower complexity under Spatial Correlated Frequency Selective(SCFS) Channel. The key of this method is after joint antennas MMSE detection (JAD/MMSE) based on interruption cancelling using soft information, considering the detection result as an output of a Gaussian equivalent flat fading channel, and performing maximum likelihood detection(ML) to get more correct estimated result. But the using of ML brings great complexity increase, which is not allowed. In this paper, a low complexity method called list sphere decoding is introduced and applied to replace the ML in order to simplify the adaptive iterative turbo equalization system.