The interpolation-based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (asd) further impro...
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The interpolation-based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (asd) further improves the decoding performance. This paper presents a unified study of two classical asd algorithms, the algebraic Chase decoding and the Koetter-Vardy decoding. Their computationally expensive interpolation is solved by the module minimisation (MM) technique which consists of basis construction and basis reduction. Compared with Koetter's interpolation, the MM interpolation yields a smaller computational cost for the two asdalgorithms. Re-encoding transform is further applied to reduce the decoding complexity by reducing the degree of module generators. Based on assessing the degree of module seeds, a complexity reducing approach is introduced to further facilitate the two asdalgorithms. Computational cost of the two algorithms as well as their re-encoding transformed variants will be analysed. Performance of the two asdalgorithms will be compared under decoding expenditure benchmark, providing more practical insights of their applications.
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