Stochastic Chase Decoding for BMS Channels via Rate Distortion Theory

2026-05-19

AI Summary

This work addresses the lack of an information-theoretic foundation in conventional stochastic Chase decoding, which relies on heuristically chosen bit-flipping probabilities. For the first time, rate-distortion theory is systematically integrated into Chase decoding over binary memoryless symmetric (BMS) channels, recasting the problem as a stochastic coding task centered on covering error patterns. An asymptotically information-theoretically optimal bit-flipping rule is derived, along with a precise characterization of the required list size. Experiments on both binary and quaternary symmetric channels demonstrate that the proposed rule closely matches the optimal strategy obtained via exhaustive search and significantly outperforms existing methods—even at short block lengths—thereby confirming both its theoretical rigor and practical efficacy.

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.

Problem

• Stochastic Chase decoding
• BMS channels
• rate distortion theory
• bit-flipping probabilities
• error-pattern covering

Innovation

• stochastic Chase decoding
• rate-distortion theory
• BMS channels
• bit-flipping rule
• error-pattern covering codes