A Rate-Distortion Perspective on Multiple Decoding Attempts for Reed-Solomon Codes

TL;DR

This paper applies a rate-distortion framework to analyze and optimize multiple decoding attempts for Reed-Solomon codes, providing insights into performance-complexity trade-offs and improving decoding algorithms.

Contribution

It introduces a novel rate-distortion perspective to analyze multiple decoding schemes for RS codes, including error-and-erasure and soft-decision decoding, enhancing understanding and performance.

Findings

Asymptotic analysis of decoding performance versus complexity.

Optimal erasure pattern selection via covering problem and rate-distortion theory.

Proposed algorithms outperform existing methods at the same complexity.

Abstract

Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these multiple-decoding algorithms for RS codes. This approach is first used to understand the asymptotic performance-versus-complexity trade-off of multiple error-and-erasure decoding of RS codes. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the condition for a single error-and-erasure decoding to succeed reduces to a form where the distortion is compared to a fixed threshold. Finding the best set of erasure patterns for multiple decoding trials then turns out to be a covering problem which can be solved asymptotically by rate-distortion theory. Next, this approach is extended to analyze multiple algebraic soft-decision (ASD) decoding of RS codes. Both analytical and numerical computations of the R-D functions for the corresponding distortion measures are discussed. Simulation results show that proposed algorithms using this approach perform better than other algorithms with the same complexity.