Proximal Decoding for LDPC Codes

Ligter, Luca

Yongchao Wang, Jing Bai

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.

Vikram Arkalgud Chandrasetty, Syed Mahfuzul Aziz

Yongchao Wang, Jing Bai

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.

Ho-Il Kim

Asahi Ito, Lantian Wei, Tadashi Wadayama

This paper introduces a deep unfolding-assisted proximal decoding for low-density parity-check (LDPC) codes. Proximal decoding method is a decoding algorithm based on the proximal gradient method. Our proposal, deep unfolding-assisted proximal (DU-Proximal) decoding, is obtained by applying deep unfolding to the proximal decoding. We especially focus on the decoding performance in multiple-input multiple-output (MIMO) channels. In numerical experiments, we compare the error correcting capability of the proposed algorithm with the minimum mean squared error (MMSE) signal detection method, the tanh signal detection method, and the MMSE jointly with belief propagation (BP) algorithm for LDPC decoding. The experimental results demonstrate that parameter optimization via DU yields significant performance gains, especially at high signal-to-noise ratio levels.