Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions

TL;DR

This paper introduces a new method for constructing LDPC codes from transversal designs based on MOLS, improving their stopping set distributions to enhance decoding performance over erasure channels.

Contribution

It develops a novel approach using combinatorial design theory to optimize LDPC codes, particularly focusing on stopping set avoidance and quasi-cyclic structures.

Findings

Improved stopping set distributions for LDPC codes from MOLS-based transversal designs.

Applicable to codes with higher column weights beyond 4.

A subclass of codes exhibits quasi-cyclic structure enabling low-complexity encoding.

Abstract

This paper examines the construction of low-density parity-check (LDPC) codes from transversal designs based on sets of mutually orthogonal Latin squares (MOLS). By transferring the concept of configurations in combinatorial designs to the level of Latin squares, we thoroughly investigate the occurrence and avoidance of stopping sets for the arising codes. Stopping sets are known to determine the decoding performance over the binary erasure channel and should be avoided for small sizes. Based on large sets of simple-structured MOLS, we derive powerful constraints for the choice of suitable subsets, leading to improved stopping set distributions for the corresponding codes. We focus on LDPC codes with column weight 4, but the results are also applicable for the construction of codes with higher column weights. Finally, we show that a subclass of the presented codes has quasi-cyclic structure which allows low-complexity encoding.