A Rate-Distortion Exponent Approach to Multiple Decoding Attempts for Reed-Solomon Codes

TL;DR

This paper introduces a rate-distortion exponent approach to optimize multiple decoding attempts of Reed-Solomon codes, providing rigorous error probability bounds and modest performance improvements.

Contribution

It applies the rate-distortion exponent analysis to Reed-Solomon decoding, enabling direct minimization of error probability decay rate and deriving a numerical method for non-identical sources.

Findings

Provides bounds on error probability for finite-length RS codes

Achieves modest performance gains over previous methods

Derives a numerical method for non-identical source rate-distortion exponent calculation

Abstract

Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides the best performance-versus-complexity trade-off. In this paper, an analysis based on the rate-distortion exponent (RDE) is used to directly minimize the exponential decay rate of the error probability. This enables rigorous bounds on the error probability for finite-length RS codes and leads to modest performance gains. As a byproduct, a numerical method is derived that computes the rate-distortion exponent for independent non-identical sources. Analytical results are given for errors/erasures decoding.