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Symbol-level iterative information set decoding of RS codes

ALEXANDRIA ENGINEERING JOURNAL 2023年 73卷 1-10页

作者： Genga, Yuval Oyerinde, Olutayo Versfeld, Jaco Univ Witwatersrand Sch Elect & Informat Engn Johannesburg South Africa Stellenbosch Univ Dept Elect & Elect Engn Matieland South Africa

This paper presents the implementation of a low-complex iterative symbol-level decoding scheme for Reed-Solomon codes. Most soft-decision iterative decoders for Reed-Solomon codes work on a bit level due to the efficient passing of soft information due to the sparsity of the binary parity check matrix. These decoders yield a good error correction performance, but this comes at the cost of an increased computational complexity resulting from working at a bit-level. This study aims to lower the computational complexity of iterative decoding of Reed-Solomon codes by intro-ducing a high-performance soft-decision iterative Reed-Solomon decoder that works on a symbol -level, in contrast to the bit-level implementation used in most iterative Reed-Solomon decoders. The proposed algorithm utilises soft information to decode while applying information set decoding techniques to an extended parity check matrix. The use of the extended parity check matrix provides additional parity check equations which assist the algorithm in determining the correct information set of symbols used in the decoding process. For a given on;k thorn Reed-Solomon code, the algorithm converges to a valid codeword by correctly decoding a specified information set of k symbols from the received vector. Simulations run show the proposed algorithm performs favourably when com-pared to other symbol-level iterative decoders while working at a relatively lower complexity.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://***/ licenses/by-nc-nd/4.0/).

关键词： Reed Solomon codes soft-input soft-output decoding Iterative decoding Message passing decoding Information set decoding decoding complexity

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An advanced low-complexity decoding algorithm for turbo product codes based on the syndrome

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EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING 2020年第1期2020卷 1-31页

作者： Yoon, Sungsik Ahn, Byungkyu Heo, Jun Korea Univ Sch Elect Engn 145 Anam Ro Seoul 02841 South Korea

This paper introduces two effective techniques to reduce the decoding complexity of turbo product codes (TPC) that use extended Hamming codes as component codes. We first propose an advanced hard-input soft-output (HISO) decoding algorithm, which is applicable if an estimated syndrome stands for double-error. In conventional soft-input soft-output (SISO) decoding algorithms, 2(p)(p: the number of least reliable bits) number of hard decision decoding (HDD) operations are performed to correct errors. However, only a single HDD is required in the proposed algorithm. Therefore, it is able to lower the decoding complexity. In addition, we propose an early termination technique for undecodable blocks. The proposed early termination is based on the difference in the ratios of double-error syndrome detection between two consecutive half-iterations. Through this early termination, the average iteration number is effectively lowered, which also leads to reducing the overall decoding complexity. Simulation results show that the computational complexity of TPC decoding is significantly reduced via the proposed techniques, and the error correction performance remains nearly the same in comparison with that of conventional methods.

关键词： Turbo product codes Syndrome-based decoding soft-input soft-output decoding Hard-input soft-output decoding Early termination

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Stochastic decoding of Linear Block Codes With High-Density Parity-Check Matrices

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第11期56卷 5733-5739页

作者： Tehrani, Saced Sharifi Jego, Christophe Zhu, Bo Gross, Warren J. McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 2A7 Canada TELECOM Bretagne CNRS Lab STICC FRE 3167 Paris France Nortel Networks Ottawa ON 3X2 B17 Canada

This correspondence extends the application of the recently proposed stochastic decoding approach to decode linear block codes with high-density parity-check matrices and discusses its hardware complexity. Results demonstrate decoding performance close to floating-point iterative soft-input soft-output (SISO) decoding while offering nodes with considerably lower complexity compared to fixed-point SISO decoding.

关键词： BCH codes block turbo codes Reed-Solomon codes soft-input soft-output decoding stochastic decoding

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Performance Limits of Compound Codes with Symbol-Based Iterative decoding

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Electronic Notes in Discrete Mathematics 2001年 6卷 433-443页

作者： Sawaya, H. Vialle, S. Boutros, J. Zémor, G. ESIB Beyrouth Mkallès B.P. 1514 Lebanon Centre de Recherche Motorola St Aubin 91193 Gif sur Yvette France ENST ComElec and InfRes Departments 75013 Paris 46 Rue Barrault France

We study the performance limit of concatenated codes based on binary constituent codes, under symbol-based iterative decoding. Although the results exposed herein are valid for any compound code built from both block and convolutional codes, we mainly focus on parallel turbo codes based on binary convolutional codes. The performance limit is found by evaluating the probability density function of the APP decoder output via a general propagation formula governing the density law through iterations. We propose also a second method to estimate the signal-to-noise ratio limit where the a priori density is assumed to be gaussian distributed. The results show that a gain in performance is achieved when bit nodes are combined into quaternary symbol nodes. For example, with a rate 1/2 Turbo code and a rate 2/3 binary RSC constituent, the minimal attainable signal-to-noise ratio per bit is 0.31 dB which is 0.13 dB away from the capacity of the AWGN channel with BPSK modulation. © 2001.

关键词： Belief propagation Concatenated codes soft-input soft-output decoding Turbo codes

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Reduced complexity maximum a posteriori decoding of variable-length codes

Reduced complexity maximum a posteriori decoding of variable...

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IEEE Global Telecommunications Conference (GLOBECOM 01)

作者： Lamy, C Pothier, O Philips Rech France PRF F-92156 Suresnes France

ISBN: (纸本)0780372069

Until very recently, joint source channel techniques mostly focused on systems using fixed-length coding, eventhough variable-length coding (VLC) is widely used, particularly in video coding. Typically, VLC bit streams are made channel-robust through packetization and standard forward-error correction (FEC). However, when the channel conditions are fairly mild, FEC can reveal itself bandwidth-inefficient. A variable-rate extension of joint source channel decoding could thus potentially replace FEC under mild conditions or, for noisier channels, could be used together with FEC to ameliorate the coding rate, extending in both cases the range of situations under which the bit stream is adequately protected. We propose here two reduced-complexity VLC soft-input decoding techniques, as well as a comparison with existing algorithms. Experimental results of a new proposed VLC decoding algorithm show very good performance and low complexity.

关键词： joint source channel decoding MAP estimation soft-input soft-output decoding variable length code

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Symbol-by-symbol decoding as an Approximation of Word-by-word decoding

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Electronic Notes in Discrete Mathematics 2001年 6卷 195-210页

作者： Battail, Gérard École Nationale Supérieure des Télécommunications (retired) F-75634 Paris Cedex 13 46 rue Barrault France

soft-input soft-output decoding consists of estimating the information symbol a posteriori probablities, taking account of the coding constraints, given the received symbol a priori probabilities. Kullback's principle of cross-entropy minimization is used for deriving optimum decoding rules assuming a linear, possibly non-systematic, binary code. A log-likelihood formalism is used throughout. Two decoding rules results, one by solving a system of analog implicit non-linear equations written in terms of a generator matrix, the other being the conventional one. We discuss simplified versions of both, present an interpretation of the first rule and compare it with the second one, given that both are intended to provide approximates of the same quantities. © 2001.

关键词： Cross-entropy minimization soft-input soft-output decoding system of analog implicit equations

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Joint channel estimation and detection using Markov chain Monte Carlo method over sparse underwater acoustic channels

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IET COMMUNICATIONS 2017年第11期11卷 1789-1796页

作者： Jing, Lianyou He, Chengbing Huang, Jianguo Ding, Zhi Northwestern Polytech Univ Sch Marine Sci & Technol Xian Shaanxi 710072 Peoples R China Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

This study proposes a novel approach to joint channel estimation and detection of orthogonal frequency division multiplexing transmission over underwater acoustic (UWA) multipath channels exhibiting cluster sparsity. Unlike most sparse channel estimations, the authors exploit the cluster-sparsity characteristic of UWA channels without additional prior information. They adopt a modified spike-and-slab prior model in their non-parametric Bayesian learning framework. To avoid the need for a closed-form Bayesian estimate, they apply the Markov chain Monte Carlo technique to joint achieve channel estimation and signal detection. The proposed solution is amenable to being integrated with soft-input soft-output decoding to improve the performance through turbo iteration. Simulation results demonstrate improved bit error rate of the proposed algorithm over existing algorithms.

关键词： error statistics Monte Carlo methods Markov processes channel estimation signal detection OFDM modulation wireless channels underwater acoustic communication multipath channels Bayes methods turbo codes iterative methods joint channel estimation and signal detection approach Markov chain Monte Carlo method sparse underwater acoustic channel orthogonal frequency division multiplexing transmission UWA multipath channels cluster sparsity sparse channel estimation modified spike-and-slab prior model nonparametric Bayesian learning framework closed-form Bayesian estimation soft-input soft-output decoding turbo iteration bit error rate

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Probability density functions of soft information

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IEEE COMMUNICATIONS LETTERS 2002年第2期6卷 52-54页

作者： Reggiani, L Tartara, G Politecn Milan Dipartimento Elettron & Informaz I-20133 Milan Italy

It is well known that soft decoding algorithms are based on the use of reliability measures for binary and nonbinary symbols. In the paper we consider an analytical estimation of the distributions of reliability measures after soft decoding of block and convolutional codes or intersymbol interference (ISI) channels. This estimation, based on a simple geometric interpretation of reliability measures, allows the observation of different distributions for correct and incorrect symbols, and could be helpful for the analysis of soft decoding algorithms.

关键词： MAP decoding soft-input soft-output decoding SOVA

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On SOVA for nonbinary codes

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IEEE COMMUNICATIONS LETTERS 1999年第12期3卷 335-337页

作者： Ling, C Wu, XF Yi, XX Nanjing Inst Commun Engn Nanjing 210016 Peoples R China

For binary codes, Fossorier et al. have shown that the soft-output Viterbi algorithm (SOVA) becomes equivalent to the Max-Log-maximum a posteriori (MAP) algorithm after a modification. In this letter, we generalize such modified SOVA to nonbinary cases, motivated by the fact that the performance gap between the original SOVA and the Max-Log-MAP algorithm broadens in these cases. The equivalence between the two algorithms is proved in a more compact form. The modified SOVA requires only add-compare-select operations and is well suited for high-speed parallel implementation.

关键词： MAP algorithm soft-input soft-output decoding SOVA

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On the Equivalence Between SOVA and Max-Log-MAP decodings

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IEEE COMMUNICATIONS LETTERS 1998年第5期2卷 137-139页

作者： Fossorier, Marc P. C. Burkert, Frank Lin, Shu Hagenauer, Joachim Univ Hawaii Dept Elect Engn Honolulu HI 96833 USA Tech Univ Munich D-80290 Munich Germany

In this letter, it is shown that after a proper simple modification, the soft-output Viterbi algorithm (SOVA) proposed by Hagenauer and Hoeher becomes equivalent to the Max-Log-maximum a posteriori ( MAP) decoding algorithm. Consequently, this modified SOVA allows to implement the Max-Log-MAP decoding algorithm by simply adjusting the conventional Viterbi algorithm. Hence, it provides an attractive solution to achieve low-complexity near-optimum soft-input soft-output decoding.

关键词： MAP decoding soft-input soft-output decoding SOVA

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