Quasi-Cyclic LDPC Codes based on Pre-Lifted Protographs

TL;DR

This paper introduces a two-step lifting method for QC-LDPC codes based on protographs, leading to improved minimum distance and girth properties over traditional one-step circulant-based liftings, verified by simulations.

Contribution

It proposes a novel two-step lifting approach for QC-LDPC codes that enhances code parameters and provides new design rules for better code performance.

Findings

Significant increase in minimum distance achieved.

Guaranteed improvement in girth compared to traditional methods.

Simulation results confirm performance enhancements.

Abstract

Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared to one-step circulant-based liftings. The expected performance improvement is verified by simulation results.