Performance enhancements for algebraic soft decision decoding of reed-solomon codes

El-Khamy, Mostafa; McEliece, Robert J.; Harel, Jonathan

doi:10.1109/isit.2004.1365456

Cited by 14 publications

(16 citation statements)

References 6 publications

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“…Other algorithms of [10] and [11] minimize the error probability directly. The algorithm of [10] (Gauss) assumes a Gaussian distribution of the score, while that of [11] (Chernoff) minimizes a Chernoff bound on the error probability. The later appears to have the best performance.…”

Section: Algebraic Soft Decodingmentioning

confidence: 99%

“…Previous multiplicity assignment algorithms [9]- [11] assumed approximate a posteriori probabilities. The problem is simplified by assuming that the transmitted codeword is drawn uniformly from .…”

Section: Hybrid Abp-asd List Decoding Algorithmmentioning

confidence: 99%

“…Koetter and Vardy (KV) [9] developed an algebraic soft-decision decoding (ASD) algorithm for RS codes based on a multiplicity assignment scheme for the GS algorithm. Alternative ASD algorithms, such as the Gaussian approximation algorithm by Parvaresh and Vardy [10] and the algorithm by El-Khamy and McEliece based on the Chernoff bound [11], [12], have better performance. Jiang and Narayanan (JN) developed an iterative algorithm based on belief propagation for soft decoding of RS codes [13], [14].…”

Section: Introductionmentioning

confidence: 99%

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Iterative algebraic soft-decision list decoding of Reed-Solomon codes

El-Khamy

McEliece

2006

IEEE J. Select. Areas Commun.

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Abstract-In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes.

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Section: Algebraic Soft Decodingmentioning

confidence: 99%

Section: Hybrid Abp-asd List Decoding Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Iterative algebraic soft-decision list decoding of Reed-Solomon codes

El-Khamy

McEliece

2006

IEEE J. Select. Areas Commun.

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“…Nevertheless, previous soft-decision decoding algorithms either can only achieve limited coding gain or have very high complexity. Algebraic soft-decision (ASD) decoding algorithms [2], [3], [4], [5], [6], [7] for RS codes have been developed recently. By incorporating the probability information from the channel into the algebraic interpolation process developed by Sudan and Guruswami [8], [9], these algorithms can achieve significant coding gain with a complexity that is polynomial with respect to the codeword length.…”

Section: Introductionmentioning

confidence: 99%

High-speed VLSI architecture for low-complexity chase soft-decision Reed-Solomon decoding

Zhang

2009

2009 Information Theory and Applications Workshop

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Abstract-Interpolation-based algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes can achieve significant coding gain with polynomial complexity. Among available ASD algorithms, the low-complexity Chase (LCC) algorithm can achieve a good performance-complexity tradeoff. In addition, the multiplicity of each interpolation point involved in this algorithm is one. These features make the LCC decoding very attractive for practical hardware implementation. In this paper, we present an efficient and high-speed VLSI architecture for the implementation of the LCC decoder. ASD algorithms have two major steps: interpolation and factorization. The high efficiency of the LCC interpolation architecture is achieved by employing a backward interpolation technique, which enables the sharing of intermediate interpolation results. We also show that the factorization step can be eliminated in the case of LCC decoding. From critical path and latency analysis, the LCC decoder can achieve a throughput of several gigabits per second in ASIC implementations. In addition, the LCC decoder requires less than three times the area of a hard-decision decoder that has the same throughput.

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“…They also showed that for codes of infinite length the best way to choose the value of m is by making it proportional to the soft information available for each point. In [6], [7] and [8] there were presented some multiplicity assignment strategies which were optimized for infinite-length codes through complex numeric algorithms. However for codes of finite length, an optimum multiplicity assignment strategy is still an open problem.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Soft-Decision Decoding of Reed-Solomon Codes with Erasures on Gaussian Channels

Coutinho¹,

Fernández²

2007

Journal of Communication and Information Systems

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Abstract-The search for increasing the error performance of algebraic soft-decision decoding of high rate Reed-Solomon (RS) codes motivates the development of this work in an attempt to determine the ultimate error-correcting capabilities of algebraic soft-decision decoding of RS codes in Gaussian channels with erasures. It is shown through simulation that a significant performance improvement can be obtained when the unreliable bits received from channel output are declared as erased bits. An alternative method to construct the reliability matrix is developed through the mapping of the a posteriori channel probabilities in order to assign equal multiplicity for symbols with the same erased bits patterns. Conversely, it is also shown through simulation that trying to declare the unreliable symbols received from the channel as erasures does not lead to any performance gain and in some cases it would affect the decoder performance.

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Performance enhancements for algebraic soft decision decoding of reed-solomon codes

Cited by 14 publications

References 6 publications

Iterative algebraic soft-decision list decoding of Reed-Solomon codes

Iterative algebraic soft-decision list decoding of Reed-Solomon codes

High-speed VLSI architecture for low-complexity chase soft-decision Reed-Solomon decoding

Algebraic Soft-Decision Decoding of Reed-Solomon Codes with Erasures on Gaussian Channels

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