Binary Diversity for Non-Binary LDPC Codes over the Rayleigh Channel

TL;DR

This paper investigates bit-interleaving strategies for non-binary LDPC codes over Rayleigh channels, proposing an optimized interleaver design that enhances performance by leveraging the code's topological structure.

Contribution

It introduces a novel optimized bit-interleaver design based on the Progressive Edge Growth algorithm for non-binary LDPC codes, improving diversity gains over Rayleigh fading channels.

Findings

Optimized interleaver outperforms random interleavers in simulations.

Regular (2,dc)-NB-LDPC codes with large girths show improved decoding thresholds.

Proposed method is adaptable to various code structures and degree distributions.

Abstract

In this paper we analyze the performance of several bit-interleaving strategies applied to Non-Binary Low-Density Parity-Check (LDPC) codes over the Rayleigh fading channel. The technique of bit-interleaving used over fading channel introduces diversity which could provide important gains in terms of frame error probability and detection. This paper demonstrates the importance of the way of implementing the bit-interleaving, and proposes a design of an optimized bit-interleaver inspired from the Progressive Edge Growth algorithm. This optimization algorithm depends on the topological structure of a given LDPC code and can also be applied to any degree distribution and code realization. In particular, we focus on non-binary LDPC codes based on graph with constant symbol-node connection $d_v = 2$. These regular $(2,dc)$-NB-LDPC codes demonstrate best performance, thanks to their large girths and improved decoding thresholds growing with the order of Finite Field. Simulations show excellent results of the proposed interleaving technique compared to the random interleaver as well as to the system without interleaver.