Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach (include convergence proofs)

TL;DR

This paper introduces two efficient proximal-ADMM decoders for nonbinary LDPC codes over Galois fields, with proven convergence and linear complexity, showing improved performance over existing decoders.

Contribution

It proposes two novel proximal-ADMM decoding algorithms for nonbinary LDPC codes, with convergence guarantees and linear complexity, enhancing decoding efficiency and effectiveness.

Findings

Both decoders are theoretically guaranteed to converge to stationary points.

Decoders have linear computational complexity per iteration.

Simulation results show improved decoding performance over state-of-the-art methods.

Abstract

In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code's length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders.