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2023 IEEE Globecom Workshops, GC Wkshps 2023

作者： Liang, Jiwei Chen, Li School of System Science and Engineering Sun Yat-sen University Guangzhou510006 China School of Electronics and Information Technology Sun Yat-sen University Guangzhou510006 China

ISBN: (纸本)9798350370218

This paper proposes the low-complexity Chase (LCC) decoding for Hermitian codes, which is facilitated by the re-encoding transform (reT) and fast factorization (FF). By identifying η unreliable received symbols, 2η test-vectors are formulated. Kotter's interpolation is performed for decoding the test-vectors, in which the common element interpolation is performed once and the uncommon element interpolation is further performed in a binary tree growing fashion. The reT is introduced to reduce its complexity and latency. Moreover, the FF is introduced to obtain the estimated codewords directly from the interpolation outcome. It eliminates the redundant encoding that identifies the most likely decoding output. Our simulation results show that the decoding complexity and latency are effectively reduced over the prototype LCC decoding of Hermitian codes. © 2023 IEEE.

关键词： factorization Hermitian codes low-complexity Chase decoding re-encoding transform

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Progressive Module Minimization for re-encoding transformed Soft Decoding of RS Codes

Progressive Module Minimization for Re-encoding Transformed ...

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IEEE International Symposium on Information Theory (ISIT)

作者： Xing, Jiongyue Chen, Li Bossert, Martin Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou Guangdong Peoples R China Sun Yat Sen Univ Sch Elect & Commun Engn Guangzhou Guangdong Peoples R China Ulm Univ Inst Commun Engn Ulm Germany

ISBN: (纸本)9781538692912

The interpolation based algebraic decoding for reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance through constructing a minimum polynomial Q(x,y) and finding its y-roots. The progressive algebraic soft decoding (PASD) constructs Q(x, y) with a progressively enlarged y-degree and terminates once the message is decoded, adapting the decoding capability and computation to the channel. This paper proposes the re-encoding transformed PASD algorithm, in which Q(x, y) is progressively constructed by the low-complexity module minimization (MM) technique. re-encoding transform (reT) results in a common divisor for polynomials of the image of the submodule basis. It can be removed, leading to a simpler image expansion and reduction. Consequently, Q(x, y) is constructed through the isomorphic image of the progressively enlarged submodule basis. Our complexity analysis characterizes the complexity reduction brought by the transform and shows high rate codes benefit a greater complexity reduction.

关键词： Module minimization progressive algebraic soft decoding reed-Solomon codes re-encoding transform

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Algebraic soft decoding of reed-Solomon codes with improved progressive interpolation

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PHYSICAL COMMUNICATION 2016年第0期20卷 48-60页

作者： Lyu, Yi Chen, Li Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China

The algebraic soft decoding (ASD) algorithm for reed-Solomon (RS) codes can correct errors beyond the half distance bound with a polynomial time complexity. However, the decoding complexity remains high due to the computationally expensive interpolation that is an iterative polynomial construction process. By performing the interpolation progressively, the progressive ASD (PASD) algorithm can adapt the decoding computation to the need, leveraging the average complexity of multiple decoding events. But the complexity reduction is realised at the expense of system memory, since the intermediate interpolation information needs to be memorised. Addressing this challenge, this paper proposes an improved PASD (I-PASD) algorithm that can alleviate the memory requirement and further reduce the decoding complexity. A condition on expanding the set of interpolated polynomials will be introduced, which excepts the need of performing iterative updates for the newly introduced polynomial. Further incorporating the re-encoding transform, the I-PASD algorithm can reduce the decoding complexity over the PASD algorithm by a factor of 1/3 and its memory requirement is at most half of the PASD algorithm. The complexity and memory requirement will be theoretically analysed and validated by numerical results. Finally, we will confirm that the complexity and memory reductions are realised with preserving the error-correction capability of the ASD algorithm. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Algebraic soft decoding Complexity reduction Koetter-Vardy algorithm re-encoding transform reed-Solomorucodes

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