Construction of LDPC convolutional codes with large girth from Latin squares

TL;DR

This paper introduces a method to construct LDPC convolutional codes with large girth using Latin squares, improving decoding performance and storage efficiency for both block and convolutional codes.

Contribution

It presents a novel construction technique for LDPC convolutional codes with girth up to 12 based on Latin squares and lifting steps, enabling compact and efficient code representations.

Findings

Constructed LDPC convolutional codes with girth up to 12.

Provided methods for efficient storage and implementation.

Applicable to both time-varying and time-invariant codes.

Abstract

Due to their capacity approaching performance low-density parity-check (LDPC) codes gained a lot of attention in the last years. The parity-check matrix of the codes can be associated with a bipartite graph, called Tanner graph. To decrease the probability of decoding failure it is desirable to have LDPC codes with large girth of the associated Tanner graph. Moreover, to store such codes efficiently, it is desirable to have compact constructions for them. In this paper, we present constructions of LDPC convolutional codes with girth up to $12$ using a special class of Latin squares and several lifting steps, which enables a compact representation of these codes. With these techniques, we can provide constructions for well-performing and efficiently storable time-varying and time-invariant LDPC convolutional codes as well as for LDPC block codes.