On the Girth of (3,L) Quasi-Cyclic LDPC Codes based on Complete Protographs

TL;DR

This paper investigates the construction of (3,L) quasi-cyclic LDPC codes from complete protographs, analyzing the minimal lifting factors needed to achieve girths of six or eight, which influence code block-length.

Contribution

It provides lower bounds on the lifting factors and block-lengths necessary for girth constraints in (3,L) QC LDPC codes derived from complete protographs.

Findings

Lower bounds on lifting factors for girth 6 and 8

Constraints on code block-lengths based on girth requirements

Analysis of complete protograph structures for LDPC code design

Abstract

We consider the problem of constructing $(3,L)$ quasi-cyclic low-density parity-check (LDPC) codes from complete protographs. A complete protograph is a small bipartite graph with two disjoint vertex sets such that every vertex in the variable-node set is connected to every vertex in the check-node set by a unique edge. This paper analyzes the required lifting factor for achieving girths of six or eight in the resulting quasi-cyclic codes with constraints on lifting. The required lifting factors provide lower bounds on the block-length of such codes.