  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.
