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 softdecoding (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 softdecoding (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 ASD algorithms. Re-encoding transform is further applied to reduce the decodingcomplexity 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 ASD algorithms. Computational cost of the two algorithms as well as their re-encoding transformed variants will be analysed. Performance of the two ASD algorithms will be compared under decoding expenditure benchmark, providing more practical insights of their applications.
Efficient quantizer design is vital in high-speed optical receivers. In this paper, the authors propose a three-level (1.5-bit) reliability-based quantizer for low-complexity soft decoding of low-density parity-check ...
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Efficient quantizer design is vital in high-speed optical receivers. In this paper, the authors propose a three-level (1.5-bit) reliability-based quantizer for low-complexity soft decoding of low-density parity-check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate-compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability-based quantizer, and it is shown that the resulting quantizer-aware LDPC codes significantly outperform other existing codes of similar rates.
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