Abstract:
In this paper, we devise new scalable decoder architectures for Reed–Solomon (RS) codes, comprising three parts: error-only decoding, error-erasure decoding, and their de...Show MoreMetadata
Abstract:
In this paper, we devise new scalable decoder architectures for Reed–Solomon (RS) codes, comprising three parts: error-only decoding, error-erasure decoding, and their decoding for singly extended RS codes. New error-only decoders are devised through algorithmic transformations of the inversionless Berlekamp–Massey algorithm (IBMA). We first generalize the Horiguchi–Koetter formula to evaluate error magnitudes using the error locator polynomial \Lambda(x) and the auxiliary polynomial B(x) produced by IBMA, which effectively eliminates the computation of error evaluator polynomial. We next devise an enhanced parallel inversionless Berlekamp–Massey algorithm (ePIBMA) that effectively takes advantage of the generalized Horiguchi–Koetter formula. The derivative ePIBMA architecture requires only 2t+1 ( t denotes the error correction capability) systolic cells, in contrast with 3t or more cells of the existing regular architectures based on IBMA or the Euclidean algorithm. Moreover, it may literally function as a linear-feedback-shift-register encoder. New error-erasure decoders are devised through algorithmic transformations of the inversionless Blahut algorithm (IBA) . The proposed split parallel inversionless Blahut algorithm (SPIBA) yields merely 2t+1 systolic cells, which is the same number as the error-only decoder ePIBMA. The task is partitioned into two separate steps, computing the complementary error erasure evaluator polynomial followed by computing error-erasure locator polynomial, both utilizing SPIBA. Surprisingly, it has exactly the same number of cells and literally the same complexity and throughput as the proposed error-only decoder architecture ePIBMA; it employs 33% less hardware and at the same time achieves more than twice faster throughput, than the serial architecture IBA. we further propose a unified parallel inversionless Blahut algorithm (UPIBA) by incorporating the key virtues of the error-only decoder ePIBMA into SPIBA. The ...
Published in: IEEE Transactions on Communications ( Volume: 63, Issue: 8, August 2015)