Optimization of Graph Based Codes for Belief Propagation Decoding

TL;DR

This paper presents a new optimization technique for designing LDPC codes by improving the Tanner graph structure to maximize belief propagation decoding thresholds, enhancing code performance.

Contribution

It introduces a novel code optimization method that limits the search space, applied to irregular and multiedge LDPC codes for better decoding thresholds.

Findings

Optimized Tanner graphs achieve higher decoding thresholds.

The technique effectively reduces randomness in the search process.

Improved LDPC codes demonstrate better error correction performance.

Abstract

A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief propagation, passes messages along the edges of this Tanner graph. Density evolution is an efficient method to analyze the performance of the belief propagation decoding algorithm for a particular LDPC code ensemble, enabling the determination of a decoding threshold. The basic problem addressed in this work is how to optimize the Tanner graph so that the decoding threshold is as large as possible. We introduce a new code optimization technique which involves the search space range which can be thought of as minimizing randomness in differential evolution or limiting the search range in exhaustive search. This technique is applied to the design of good irregular LDPC codes and multiedge type LDPC codes.