A Low-Complexity Bit-Embedding Decoder for Non-Binary LDPC Codes in $\mathbb {F}_{2^{q}}$

In this letter, a new decoder based on a bit-embedding technique for non-binary low-density parity-check (LDPC) codes over Galois fields of characteristic two ($\mathbb {F}_{2^{q}}$) is presented. The main content of this work is summarized in the following: first, we derive the equivalent binary codeword and binary parity-check matrix for non-binary LDPC codes in $\mathbb {F}_{2^{q}}$; second, a customized belief propagation algorithm utilizing a bit-embedding technique is proposed based on the formulated binary-check matrix; in the end, simulations results demonstrate that the proposed approach enjoys significant improvement on computational complexity, but almost similar error-correction performance in comparison with the state-of-the-art non-binary LDPC decoders.