  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.
