论文标题
通过近端ADMM方法解码非二进制LDPC代码（包括收敛证明）
Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach (include convergence proofs)
论文作者
论文摘要
在本文中，我们专注于通过乘数的近端交替方向方法（近端-ADMM）的近端交替方向方法解码特征两的GALOIS字段中的非二进制低密度平价检查（LDPC）代码。通过利用Flanagan/基于三变量奇迹检查方程的Flanagan/常数加权嵌入技术和分解技术，提出了两个有效的非二进制LDPC代码的有效近端ADMM解码器。我们表明，从理论上讲，这两个都可以保证收敛到解码模型的某个固定点，并且它们在每个近端ADMM迭代中的计算复杂性都与LDPC代码的长度和所考虑的Galois字段的大小线性缩放。此外，基于恒定嵌入技术的解码器满足了密码字对称的有利属性。模拟结果证明了它们与最先进的LDPC解码器相比的有效性。
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.
