An Interpolation Procedure for List Decoding Reed–Solomon Codes Based on Generalized Key Equations

Alexander Zeh, Christian Gentner, Daniel Augot
2011 IEEE Transactions on Information Theory  
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
more » ... rpolation 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 , our algorithm has time complexity s^4n^2.
doi:10.1109/tit.2011.2162160 fatcat:2ipefyqnsvavvjffk6wwsc75sq