Multiplicatively Repeated Non-Binary LDPC Codes

TL;DR

This paper introduces a new class of non-binary LDPC codes created by multiplicative repetition, achieving better performance at lower rates than binary counterparts, with decoding complexity similar to the original code.

Contribution

It presents a novel method to construct rate-compatible non-binary LDPC codes with improved performance and efficient decoding algorithms.

Findings

Lower-rate codes outperform binary LDPC codes

Decoding complexity remains similar to the mother code

Constructs a family of rate-compatible codes

Abstract

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform the best low-rate binary LDPC codes so far. Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.