Article
A Parametric Approach to List Decoding of ReedSolomon Codes Using Interpolation
Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia
IEEE Transactions on Information Theory (Impact Factor: 2.62). 11/2011; DOI: 10.1109/TIT.2011.2165803 Source: arXiv

Conference Paper: A progressive interpolation approach for GuruswamiSudan algorithm
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ABSTRACT: In this paper, we present a progressive interpolation approach in GuruswamiSudan (GS) decoding of ReedSolomon (RS) codes. The objective of the interpolation is to construct the minimal polynomial Q(x, y) by the progressive approach with increasing multiplicities until the roots of Q(x, y) give the correct message. Then the errorcorrection capability can be adaptively obtained by assigning a suitable multiplicity according to the number of errors occurred in the channel. We present an efficient way to update the polynomial set utilizing the previous computational results in the interpolation step. It enables the decoder to adjust its decoding complexity to the needed level. Simulation results suggest that the average decoding complexity of GS algorithm can be significantly reduced by the progressive approach for RS codes.Communication Technology (ICCT), 2012 IEEE 14th International Conference on; 01/2012  [Show abstract] [Hide abstract]
ABSTRACT: We derive the Wu listdecoding algorithm for Generalised ReedSolomon (GRS) codes by using Gr\"obner bases over modules and the Euclidean algorithm (EA) as the initial algorithm instead of the BerlekampMassey algorithm (BMA). We present a novel method for constructing the interpolation polynomial fast. We give a new application of the Wu list decoder by decoding irreducible binary Goppa codes up to the binary Johnson radius. Finally, we point out a connection between the governing equations of the Wu algorithm and the GuruswamiSudan algorithm (GSA), immediately leading to equality in the decoding range and a duality in the choice of parameters needed for decoding, both in the case of GRS codes and in the case of Goppa codes.IEEE Transactions on Information Theory 11/2012; · 2.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Minimal list decoding for a code C refers to list decoding with radius L(y), where L(y) is the minimum of the distances between the received word y and any codeword in C. In this paper we present a minimal list decoding algorithm for Reed Solomon (RS) codes. Our approach involves a parametrization of the interpolating polynomials of a minimal Gr¨ obner basis G. We then demonstrate that our parametric approach can be solved by a computationally efficient rational curve fitting solution from a recent paper by Wu. Besides, we present an algorithm to compute the minimum multiplicity as well as the associated optimal values of the parameters. Use of these optimal parameters in the rational interpolation step results in computational as well as memory efficiency.01/2011;
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