Design of Multiple-Edge Protographs for QC LDPC Codes Avoiding Short Inevitable Cycles

TL;DR

This paper introduces a systematic design method for multiple-edge protographs in QC LDPC codes, avoiding short inevitable cycles and achieving larger minimum Hamming distances, with improved girth and performance.

Contribution

It fully investigates subgraph patterns causing inevitable cycles in multiple-edge protographs and proposes new construction algorithms for QC LDPC codes with girth at least 12 and 14.

Findings

Codes with larger girth and minimum Hamming distance.

Proposed codes outperform PEG-based LDPC codes.

Systematic construction method for multiple-edge protographs.

Abstract

There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them are focused on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple edges. Compared to single-edge protographs, multiple-edge protographs have benefits such that QC LDPC codes lifted from them can potentially have larger minimum Hamming distance. In this paper, all subgraph patterns of multiple-edge protographs, which prevent QC LDPC codes from having large girth by inducing inevitable cycles, are fully investigated based on graph-theoretic approach. By using combinatorial designs, a systematic construction method of multiple-edge protographs is proposed for regular QC LDPC codes with girth at least 12 and also other method is proposed for regular QC LDPC codes with girth at least 14. A construction algorithm of QC LDPC codes by lifting multiple-edge protographs is proposed and it is shown that the resulting QC LDPC codes have larger upper bounds on the minimum Hamming distance than those lifted from single-edge protographs. Simulation results are provided to compare the performance of the proposed QC LDPC codes, the progressive edge-growth (PEG) LDPC codes, and the PEG QC LDPC codes.