Quasi Cyclic LDPC Codes Based on Finite Set Systems

TL;DR

This paper introduces a new class of Quasi-cyclic LDPC codes based on finite set systems that achieve large girth, high rates, and excellent performance over AWGN channels, advancing coding theory and design.

Contribution

It proposes FSS-based Quasi-cyclic LDPC codes with large girth and arbitrary column weights, offering higher rates and better performance than existing geometric and cylinder-type codes.

Findings

FSS codes have large girth and high rates.

FSS codes outperform random-like LDPC codes in simulations.

FSS codes show significant coding gains over AWGN channels.

Abstract

A finite set system (FSS) is a pair (V; B) where V is a finite set whose members are called points, equipped with a finite collection of its subsets B whose members are called blocks. In this paper, finite set systems are used to define a class of Quasi-cyclic low- density parity-check (LDPC) codes, called FSS codes, such that the constructed codes possess large girth and arbitrary column-weight distributions. Especially, the constructed column weight-2 FSS codes have higher rates than the column weight-2 geometric and cylinder-type codes with the same girths. To find the maximum girth of FSS codes based on (V; B), inevitable walks are defined in B such that the maximum girth is determined by the smallest length of the inevitable walks in B. Simulation results show that the constructed FSS codes have very good performance over the AWGN channel with iterative decoding and achieve significantly large coding gains compared to the random-like LDPC codes of the same lengths and rates.