论文标题
非二进制LDPC代码的近端ADMM解码器
Proximal-ADMM Decoder for Nonbinary LDPC Codes
论文作者
论文摘要
在本文中，我们通过Galois字段中的非二元线性块代码的乘数（近端ADMM）技术开发了有效的解码器。它的主要内容如下：首先，基于三变量检查方程来利用分解技术，我们将最大似然（ML）解码问题大约在非convex二次程序中；其次，提出了基于近端ADMM技术的有效算法来解决公式的QP问题。利用QP问题的固有结构，可以并行更新其变量；第三，我们证明所提出的解码算法可以收敛到公式化QP问题的某个固定点。此外，我们还显示，对于非二进制低密度奇偶校验检查（LDPC）代码，其在每个近端ADMM迭代中的计算复杂性与块长度和所考虑的Galois场的大小线性缩放。仿真结果表明，就误差校正性能或计算复杂性而言，所提出的近端-ADMM解码器优于最先进的非二元LDPC解码器。
In this paper, we develop an efficient decoder via the proximal alternating direction method of multipliers (proximal-ADMM) technique for nonbinary linear block codes in the Galois field. Its main contents are as follows: first, exploiting the decomposition technique based on the three-variables check equation, we formulate the maximum likelihood (ML) decoding problem approximately to a non-convex quadratic program; second, an efficient algorithm based on the proximal-ADMM technique is proposed to solve the formulated QP problem. Exploiting the QP problem's inherent structures, its variables can be updated in parallel; third, we prove that the proposed decoding algorithm can converge to some stationary point of the formulated QP problem. Moreover, we also show, for nonbinary low-density parity-check (LDPC) codes, its computational complexity in each proximal-ADMM iteration scales linearly with block length and the size of the considered Galois field. Simulation results demonstrate that the proposed proximal-ADMM decoder outperforms state-of-the-art nonbinary LDPC decoders in terms of either error correction performance or computational complexity.
