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A New list decoding algorithm for Short-Length TBCCs With CRC

IEEE ACCESS 2018年 6卷 35105-35111页

作者： Kim, Jae-Won Tak, Jun-Woo Kwak, Hee-Youl No, Jong-Seon Seoul Natl Univ INMC Dept Elect & Comp Engn Seoul 08826 South Korea

In this paper, a new list decoding algorithm for tail-biting convolutional codes (TBCCs) with a cyclic redundancy check (CRC) is proposed, where the CRC is considered as a concatenated outer code. The main idea of the proposed algorithm is to modify the list decoding procedure of the TBCC by using the CRC. Two algorithms are proposed for the list decoding of the TBCC with the CRC. The first proposed algorithm is a new initial state estimating algorithm using re-encoded CRC bits and having the low computational complexity. The other proposed algorithm is a modified list Viterbi algorithm, where trellis paths are fixed by re-encoded CRC bits and some CRC bits are used for the error correction. For the TBCC concatenated with the CRC code defined in the long-term evolution standard, the proposed decoding scheme by partially using CRC bits outperforms the conventional list decoding algorithms for the list size L = 4 even though the proposed algorithm has the lower decoding complexity.

关键词： Cyclic redundancy check (CRC) list decoding algorithm list Viterbi algorithm (LVA) tail-biting convolutional codes (TBCCs) Viterbi algorithm

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Symbol-Decision Successive Cancellation list Decoder for Polar Codes

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第3期64卷 675-687页

作者： Xiong, Chenrong Lin, Jun Yan, Zhiyuan Lehigh Univ Dept Elect & Comp Engn Bethlehem PA 18015 USA Nanjing Univ Sch Elect Sci & Engn Nanjing 210008 Jiangsu Peoples R China

Polar codes are of great interests because they provably achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes while having an explicit construction. Most existing decoding algorithms of polar codes are based on bit-wise hard or soft decisions. In this paper, we propose symbol-decision successive cancellation (SC) and successive cancellation list (SCL) decoders for polar codes, which use symbol-wise hard or soft decisions for higher throughput or better error performance. First, we propose to use a recursive channel combination to calculate symbol-wise channel transition probabilities, which lead to symbol decisions. Our proposed recursive channel combination has lower complexity than simply combining bit-wise channel transition probabilities. The similarity between our proposed method and Arikan's channel transformations also helps to share hardware resources between calculating bit-and symbol-wise channel transition probabilities. Second, a two-stage list pruning network is proposed to provide a trade-off between the error performance and the complexity of the symbol-decision SCL decoder. Third, since memory is a significant part of SCL decoders, we propose a pre-computation memory-saving technique to reduce memory requirement of an SCL decoder. Finally, to evaluate the throughput advantage of our symbol-decision decoders, we design an architecture based on a semi-parallel successive cancellation list decoder. In this architecture, different symbol sizes, sorting implementations, and message scheduling schemes are considered. Our synthesis results show that in terms of area efficiency, our symbol-decision SCL decoders outperform existing bit-decision and multi-bit SCL decoders.

关键词： Error control codes hardware implementation list decoding algorithm polar codes successive cancellation

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Soft decision iterative error and erasure decoder for Reed-Solomon codes

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IET COMMUNICATIONS 2014年第16期8卷 2863-2870页

作者： Ur-Rehman, Obaid Zivic, Natasa Univ Siegen Chair Data Commun Syst D-57076 Siegen Germany

A list decoding algorithm for iterative soft-decision decoding of Reed-Solomon (RS) codes is proposed in this study. The algorithm erases a combination of least reliable symbols and iteratively flips a new combination of least reliable bits in the received sequence. The symbol error correction capability of the algebraic hard decision RS decoder is extended up to the minimum Hamming distance of the code. A gain in performance is exhibited either at a lower or similar iteration complexity as compared to other iterative soft decision decoders of similar type. A complexity comparison with some of the comparable soft decision decoders is given. Simulation results for different modulation schemes and channel types are presented in this study for a comparison with other soft decision decoders of a similar kind.

关键词： iterative decoding Reed-Solomon codes algebraic codes soft decision iterative error erasure decoder Reed-Solomon codes list decoding algorithm iterative soft decision decoding least reliable symbols received sequence symbol error correction capability algebraic hard decision RS decoder minimum Hamming distance iteration complexity

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A modified Guruswami-Sudan algorithm for decoding Reed-Solomon codes

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INFORMATION PROCESSING LETTERS 2010年第22期110卷 992-997页

作者： Wang, Xiaorong Shi, Hongbo Nanjing Univ Finance & Econ Dept Appl Math Nanjing 210046 Peoples R China

We tighten a key estimate, which dictates the computational complexity of Guruswami-Sudan algorithm, on the lower bound of the degrees of freedom, and then propose a modified decoding algorithm for Reed-Solomon codes beyond half the minimum distance. The computational complexity of the modified algorithm is lower than the Guruswami-Sudan algorithm for the medium to high rate Reed-Solomon codes, and has the same asymptotic complexity as the algorithm proposed by Wu. Besides we also claim that our modified algorithm outperforms Wu's algorithm to some extent. (C) 2010 Elsevier By. All rights reserved.

关键词： Reed-Solomon codes list decoding algorithm Design of algorithms Computational complexity

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On the list and bounded distance decodability of Reed-Solomon codes

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SIAM JOURNAL ON COMPUTING 2007年第1期37卷 195-209页

作者： Cheng, Qi Wan, Daqing Univ Oklahoma Sch Comp Sci Norman OK 73019 USA Univ Calif Irvine Dept Math Irvine CA 92697 USA Chinese Acad Sci Inst Math Beijing 100080 Peoples R China

For an error-correcting code and a distance bound, the list decoding problem is to compute all the codewords within a given distance to a received message. The bounded distance decoding problem is to find one codeword if there is at least one codeword within the given distance, or to output the empty set if there is not. Obviously the bounded distance decoding problem is not as hard as the list decoding problem. For a Reed-Solomon code [n, k](q), a simple counting argument shows that for any integer 0 < g < n, there exists at least one Hamming ball of radius n-g, which contains at least ((n)(g))/q(g-k) many codewords. Let (g) over cap (n, k, q) be the smallest positive integer g such that (g(n))/q(g-k) <= 1. One knows that k - 1 <= (g) over bar (n, k, q) <= root n(k-1) <= n. For the distance bound up to n - root n(k - 1), it is known that both the list and bounded distance decoding can be solved e. ciently. For the distance bound between n- root n(k - 1) and n-(g) over bar (n, k, q), we do not know whether the Reed - Solomon code is list or bounded distance decodable;nor do we know whether there are polynomially many codewords in all balls of the radius. It is generally believed that the answer to both questions is no. In this paper, we prove the following: ( 1) list decoding cannot be done for radius n-(g) over cap (n, k, q) or larger, unless the discrete logarithm over F-q (g) double under bar (n,F- k,F- q)- k is easy. (2) Let h and g be positive integers satisfying q >= max(g(2), (h - 1)(2+is an element of)) and g = (4/is an element of + 2)(h+1) for a constant is an element of > 0. We show that the discrete logarithm problem over F-q(h) can be e. ciently reduced by a randomized algorithm to the bounded distance decoding problem of the Reed-Solomon code [q, g-h](q) with radius q - g. These results show that the decoding problems for the Reed-Solomon code are at least as hard as the discrete logarithm problem over certain finite fields. For the list decoding proble

关键词： list decoding algorithm bounded distance decoding algorithm Reed-Solomon codes discrete logarithm problem

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On the list and bounded distance decodability of Reed-Solomon codes

On the list and bounded distance decodability of Reed-Solomo...

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45th Annual IEEE Symposium on Foundations of Computer Science

作者： Cheng, Qi Wan, Daqing Univ Oklahoma Sch Comp Sci Norman OK 73019 USA Univ Calif Irvine Dept Math Irvine CA 92697 USA Chinese Acad Sci Inst Math Beijing 100080 Peoples R China

关键词： list decoding algorithm bounded distance decoding algorithm Reed-Solomon codes discrete logarithm problem

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Reed-Solomon Codes as Traceability Codes with an Efficient Tracing algorithm

Reed-Solomon Codes as Traceability Codes with an Efficient T...

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2006 8th International Conference on Signal Processing

作者： Yizhou Ma Yuewei Ding College of Computer Engineering University of Shanghai for Science and Technology

ISBN: (纸本)0780397371

Traitor tracing is one kind of piracy deterrent schemes that helps trace the source of leaks when sensitive or proprietary data is made available to a large set of *** their natural properties,error correcting codes can be applied as traceability codes in such *** this paper,we present ReedSolomon codes as a kind of traceability codes and use list decoding algorithm to efficiently trace the traitors. We emphasize the conditions under which list decoding algorithm can be applied successfully for Reed-Solomon codes and the maximum numbers of users and traceable traitors for particular codes.

关键词： Traitor Tracing Reed-Solomon codes Traceability Codes list decoding algorithm

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