New Algebraic Soft Decision Decoding Algorithm for Reed-Solomon Code

TL;DR

This paper introduces a novel algebraic soft-decision decoding algorithm for Reed-Solomon codes that utilizes rational interpolation and a new factorization approach, improving decoding efficiency over traditional methods.

Contribution

The paper presents a new decoding algorithm based on rational interpolation and a specialized factorization technique, differing from the K{"o}tter-Vardy algorithm.

Findings

Requires interpolation for two smaller multiplicity matrices

Uses Berlekamp-Messay algorithm for constructing interpolation points

Potentially reduces computational complexity

Abstract

In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional K{\"o}tter-Vardy algorithm, new algorithm needs interpolation for two smaller multiplicity matrixes, due to the corresponding factorization algorithm for re-constructing codewords.