Quasi-BP for BCH Codes and its Optimization

TL;DR

This paper introduces a quasi-belief propagation decoder for BCH codes that leverages domain knowledge and information-theoretic analysis to enhance decoding efficiency and performance, approaching that of LDPC codes.

Contribution

It formalizes a novel, parallelizable decoding scheme for BCH codes using EXIT charts and mutual information tracking, enabling near-LDPC performance with high-density parity-check codes.

Findings

Decoder performance approaches LDPC codes with similar rate and blocklength.

The scheme is robust across various code rates and lengths.

Mutual information evolution validates the optimization process.

Abstract

This paper proposes a quasi-belief propagation decoder for BCH codes that systematically integrates domain knowledge--specifically, channel noise variance, the cyclic property of the codes, and the deliberate redundancy in their parity-check matrices--to enable efficient iterative decoding. We rigorously formalize this parallelizable decoder within an information-theoretic framework by tracking mutual information evolution through the constituent variable and check decoders, thereby validating the use of scattered EXIT charts as a tool for optimizing the decoder's parameters. At each iteration, an input dilation operation expands the set of messages, while a subsequent merging operation accelerates mutual information growth, ensuring rapid convergence. The proposed decoder achieves decoding performance approaching that of LDPC codes with comparable rate and blocklength, effectively pioneering the feasible deployment of BP-like decoding for high-density parity-check codes. The generality and robustness of the scheme are demonstrated through extensive simulations across codes of varying rates and blocklengths.