Structured LDPC Codes from Permutation Matrices Free of Small Trapping Sets

TL;DR

This paper proposes a new class of structured LDPC codes using permutation matrices derived from Latin squares, designed to eliminate small trapping sets and improve decoding performance on BSC and AWGNC.

Contribution

It introduces a novel construction of LDPC codes with permutation matrices from Latin squares that avoid harmful subgraphs, enhancing decoding reliability.

Findings

Codes exhibit excellent error performance on BSC and AWGNC

Construction effectively eliminates small trapping sets

Codes are optimized for Gallager A/B algorithms

Abstract

This paper introduces a class of structured lowdensity parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance is very good on the additive white Gaussian noise channel (AWGNC) as well.