Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes

TL;DR

This paper introduces an iterative soft-decision list decoding algorithm for Reed-Solomon codes that combines algebraic and belief-propagation techniques, achieving improved performance and reduced complexity.

Contribution

It presents a novel iterative decoding approach that integrates algebraic soft-decision decoding with belief propagation, enhancing efficiency and decoding capability.

Findings

Reduced computational complexity compared to previous methods

Improved decoding performance with iterative approach

Effective combination of algebraic and belief-propagation techniques

Abstract

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of Reed-Solomon codes.