Fast factorization architecture in soft-decision Reed-Solomon decoding
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
List decoding of Hermitian codes using Gröbner bases
Journal of Symbolic Computation
Soft-decision list decoding of hermitian codes
IEEE Transactions on Communications
Algebraic soft-decision decoding of Hermitian codes
IEEE Transactions on Information Theory
M-ary hyper phase-shift keying with Reed Solomon encoding and soft decision reliability information
MILCOM'09 Proceedings of the 28th IEEE conference on Military communications
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A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound. In previous work by M. Shokrollahi and H. Wasserman (see ibid., vol.45, p.432-7, March 1999) a list-decoding procedure for Reed-Solomon codes was generalized to algebraic-geometric codes. Recent work by V. Guruswami and M. Sudan (see ibid., vol.45, p.1757-67, Sept. 1999) gives improved list decodings for Reed-Solomon codes and algebraic-geometric codes that work for all rates and have many applications. However, these list-decoding algorithms are rather complicated. R. Roth and G. Ruckenstein (see ibid., vol.46, p.246-57, Jan. 2000) proposed an efficient implementation of the list decoding of Reed-Solomon codes. In this correspondence, extending Roth and Ruckenstein's fast algorithm for finding roots of univariate polynomials over polynomial rings, i.e., the reconstruct algorithm, we present an efficient algorithm for finding the roots of univariate polynomials over function fields. Based on the extended algorithm, we give an efficient list-decoding algorithm for algebraic-geometric codes