Efficient ADMM Decoder for Non-binary LDPC Codes with Codeword-Independent Performance

TL;DR

This paper introduces an efficient ADMM-based decoding algorithm for non-binary LDPC codes over GF(2^q), achieving lower complexity and codeword-independent performance, with superior simulation results.

Contribution

The paper proposes a novel ADMM decoding algorithm for non-binary LDPC codes that reduces complexity and ensures codeword-independent performance.

Findings

Lower computational complexity per iteration (~O(nq))

Achieves codeword-independent decoding performance

Outperforms existing LDPC decoders in simulations

Abstract

In this paper, we devote to devise a non-binary low-density parity-check (LDPC) decoder in Galois fields of characteristic two ($\mathbb{F}_{2^q}$) via the alternating direction method of multipliers (ADMM) technique. Through the proposed bit embedding technique and the decomposition technique of the three-variables parity-check equation, an efficient ADMM decoding algorithm for non-binary LDPC codes is proposed. The computation complexity in each ADMM iteration is roughly $\mathcal{O}(nq)$, which is significantly lower than the existing LDPC decoders. Moreover, we prove that the proposed decoder satisfies the favorable property of the codeword-independent. Simulation results demonstrate the outstanding performance of the proposed decoder in contrast with state-of-the-art LDPC decoders.