[show abstract][hide abstract] ABSTRACT: The key step of syndrome-based decoding of Reed-Solomon codes up to half the minimum distance is to solve the so-called Key Equation. List decoding algorithms, capable of decoding beyond half the minimum distance, are based on interpolation and factorization of multivariate polynomials. This article provides a link between syndrome-based decoding approaches based on Key Equations and the interpolation-based list decoding algorithms of Guruswami and Sudan for Reed-Solomon codes. The original interpolation conditions of Guruswami and Sudan for Reed-Solomon codes are reformulated in terms of a set of Key Equations. These equations provide a structured homogeneous linear system of equations of Block-Hankel form, that can be solved by an adaption of the Fundamental Iterative Algorithm. For an (n,k) Reed-Solomon code, a multiplicity s and a list size l , our algorithm has time complexity O(ls4n2).
IEEE Transactions on Information Theory 01/2011; 57(2011-09-9):5946-5959. · 2.62 Impact Factor
[show abstract][hide abstract] ABSTRACT: In this paper we propose a new algorithm that solves the Guruswami-Sudan interpolation step for Reed-Solomon codes efficiently. It is a generalization of the Feng-Tzeng approach, the so-called fundamental iterative algorithm. From the interpolation constraints of the Guruswami-Sudan principle it is well known that an improvement of the decoding radius can only be achieved, if the multiplicity parameter s is smaller than the list size l. The code length is n and our proposed algorithm has a complexity (without asymptotic assumptions) of O(ls<sup>4</sup> n<sup>2</sup>).
Information Theory Workshop, 2009. ITW 2009. IEEE; 11/2009