Stochastic Chase Decoding for BMS Channels via Rate Distortion Theory

TL;DR

This paper introduces a rate-distortion-based, information-theoretic approach to stochastic Chase decoding for algebraic codes over BMS channels, replacing heuristics with optimal flipping rules grounded in theory.

Contribution

It adapts rate-distortion theory to design explicit, asymptotically optimal bit-flip probabilities for Chase decoding, improving decoding efficiency and accuracy.

Findings

Optimal flipping rules closely match information-theoretic rules at short block lengths.

The approach provides explicit characterization of the expected list size.

The method generalizes previous frameworks to BMS channels.

Abstract

This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with information-theoretically grounded flipping rules. In particular, we reinterpret stochastic Chase decoding as a random-coding construction for error-pattern covering codes. Our approach builds on the framework of Nguyen et al., who introduced a rate-distortion formulation of multiple-attempt decoding for Reed-Solomon codes over nonbinary channels. In their formulation, erasure patterns are generated so as to align with, and thereby mask, hard-decision errors. We adapt this framework to the design of bit-flip probabilities for Chase decoding over BMS channels. This yields an explicit characterization of the asymptotically optimal bit-flipping rule, together with the expected list size required to ensure that the transmitted codeword appears in the decoding list with high probability. Moreover, for binary and quaternary symmetric channels, we demonstrate that the optimal bit-flipping rule, determined by exhaustive search, closely matches the information-theoretic rule even at short block lengths.