Double Cylinder Cycle codes of Arbitrary Girth

TL;DR

This paper introduces a new class of low-density parity-check codes called double cylinder cycle codes, which achieve higher rates than previous cycle codes with the same girth by utilizing a novel graph representation.

Contribution

It proposes a new graph-based approach to construct double cylinder-type parity-check matrices that improve code rate while maintaining girth, advancing the design of LDPC codes.

Findings

Higher code rates for given girth compared to previous codes

Introduction of block-structure graph for analyzing code properties

Construction of mother matrices with column-weight two

Abstract

A particular class of low-density parity-check codes referred to as cylinder-type BC-LDPC codes is proposed by Gholami and Eesmaeili. In this paper We represent a double cylinder-type parity-check matrix H by a graph called the block-structure graph of H and denoted by BSG(H). Using the properties of BSG(H) we propose some mother matrices with column-weight two such that the rate of corresponding cycle codes are greater tan cycle codes constructed by Gholami with same girth.