Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes with Large Girth

TL;DR

This paper introduces a low-complexity approach for designing compact QC-LDPC and SC-LDPC convolutional codes with large girth, improving code length and performance over classical methods.

Contribution

A novel low-complexity method for constructing compact QC-LDPC and SC-LDPC codes with large girth and reduced syndrome former lengths.

Findings

Codes with girth 10 or 12 achieved

Shorter code lengths than classical designs

Numerical examples demonstrate effectiveness

Abstract

We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and shorter length than those designed through classical approaches. The method is extended to time-invariant spatially coupled low-density parity-check convolutional codes, permitting to achieve small syndrome former constraint lengths. Several numerical examples are given to show its effectiveness.