Constructing LDPC Codes from Partition and Latin-Style Splicing

TL;DR

This paper introduces a new method for constructing longer LDPC codes with guaranteed girth properties by partitioning and splicing shorter codes based on Latin squares, resulting in codes with improved performance.

Contribution

A novel, general method for constructing longer LDPC codes from shorter ones using Latin square-based splicing, ensuring girth nondecreasing and better performance.

Findings

Longer LDPC codes with girth at least eight achieved

Method includes existing approaches as special cases

Codes demonstrate satisfactory performance in simulations

Abstract

A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping components with the same size. Then, these components are combined together to form the parity-check matrix of a longer code, according to a given N*N Latin square. To illustrate this method, longer quasi-cyclic (QC) LDPC codes are obtained with girth at least eight and satisfactory performance, via shorter QC-LDPC codes with girth eight but poor performance. The proposed method naturally includes several well-known methods as special cases, but is much more general compared with these existing approaches.