An ontology-based approach to the optimization of non-binary (2,v)-regular LDPC codes

TL;DR

This paper presents an ontology-based method to optimize non-binary (2,v)-regular LDPC codes by analyzing cycle patterns to improve their distance properties and design codes with better minimum bit-distance.

Contribution

It introduces an ontology framework for identifying cycle patterns in non-binary LDPC codes to facilitate their optimization and code design.

Findings

Analyzed three CCSDS recommended codes.

Designed several codes with improved minimum bit-distance.

Provided a systematic approach for code optimization.

Abstract

A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected cycle patterns that lead to low symbol-weight codewords are identified to put together the ontology. The optimization goal is to improve the distance property of equivalent binary images. Using the proposed method, the estimation and optimization of bit-distance spectrum becomes easily handleable. Three codes in the CCSDS recommendation are analyzed and several codes with good minimum bit-distance are designed.