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New list decoding algorithms for Reed-Solomon and BCH codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第8期54卷 3611-3630页

作者： Wu, Yingquan Link A Media Devices Corp Santa Clara CA USA

In this paper, we devise a rational curve fitting algorithm and apply it to the list decoding of Reed-Solomon and Bose-Chaudhuri-Hocquenghen (BCH) codes. The resulting list decoding algorithms exhibit the following significant properties. The algorithm achieves the limit of list error correction capability (LECC)n(1-root 1-D) for a (generalized) (n, k, d = n-k+1) Reed-Solomon code, which matches the Johnson bound, where D =Delta d/n denotes the normalized minimum distance. The algorithmic complexity is O (n(6)(1-root 1-D)(8)). In comparison with the Guruswami-Sudan algorithm, which exhibits the same LECC, the proposed requires a multiplicity (which dictates the algorithmic complexity) significantly smaller than that of the Guruswami-Sudan algorithm in achieving a given LECC, except for codes with code-rate below 0.15. In particular, for medium-to-high rate codes, the proposed algorithm reduces the multiplicity by orders of magnitude. Moreover, for any epsilon > 0, the intermediate LECC t = left perpendicular 1/epsilon right perpendicular. Its list size is shown to be upper bounded by a constant with respect to a fixed normalized minimum distance D, rendering the algorithmic complexity quadratic in nature, O(n(2)). By utilizing the unique properties of the Berlekamp algorithm, the algorithm achieves the LECC limit n/2 (1-root 1 - 2D) for a narrow-sense (n, k, d) binary BCH code, which matches the Johnson bound for binary codes. The algorithmic complexity is O (n(6)(1-root 1-2D)(8)). Moreover, for any epsilon > 0, the intermediate LECC t = left perpendicular epsilon . d/2 + (1 - epsilon) . n-root n(n-2d)/2 right perpendicular can be achieved by the proposed algorithm with multiplicity m = left perpendicular 1/2 epsilon right perpendicular. Its list size is shown to be upper bounded by a constant, rendering the algorithmic complexity quadratic in nature, O(n(2)).

关键词： Berlekamp algorithm Berlekamp-Massey algorithm binary Bose-Chaudhuri-Hocquenghen (BCH) codes Johnson bound list decoding rational curve-fitting algorithm Reed-Solomon codes

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New list decoding algorithms for Reed-Solomon and BCH codes

New list decoding algorithms for Reed-Solomon and BCH codes

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IEEE International Symposium on Information Theory

作者： Wu, Yingquan Link A Media Devices Corp Santa Clara CA USA

ISBN: (纸本)1424414296

关键词： Berlekamp algorithm Berlekamp-Massey algorithm binary Bose-Chaudhuri-Hocquenghen (BCH) codes Johnson bound list decoding rational curve-fitting algorithm Reed-Solomon codes

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