【摘要】 针对高速航空通信场景中的衰落和干扰使得传输数据易错误或丢失这一问题，提出一种在伽罗华域F_2^q上的多元低密度奇偶校验（LDPC）码的交替方向乘子法（ADMM）译码器。首先，利用提出的比特嵌入技术，将多元LDPC码等价转化为二元LDPC码，并基于此将多元最大似然（ML）译码问题转化为实空间中的线性整数规划问题。其次，将整数约束问题松弛为连续约束问题，为目标函数添加非凸二次惩罚项，并定制了一种高效的ADMM算法来求解译码模型，其中所有变量都可以并行求解。最后，证明了提出的ADMM译码器满足重要的码字独立特性，且每次ADMM迭代中的计算复杂度约为O（nq）。实验结果表明提出的译码器的纠错能力和译码效率优于其他译码器。更多还原

【Abstract】 Aimed at the problems that transmission data is liable to make mistakes or to lose caused by fading and interference in high-speed aviation communication scenario, a new alternating direction method of multipliers decoder for non-binary low-density parity-check codes in Galois fields F_2^q is proposed. Firstly, a bit embedding rule is proposed, and the procedure of formulating the maximum likelihood decoding problem to a linear integer problem in real space is presented. Secondly, after relaxing the integer problem to a continuous one, an efficient ADMM algorithm is customized to solve the latter, where all the entries of the variable vectors can be obtained in parallel. Thirdly, it is important that the proposed ADMM decoder sa-tisfies the needs of favorable codeword-independent property under some mild conditions and its computation complexity in each ADMM iteration is roughly O（nq）. The simulation results show that this ADMM decoder is prior to the others in error-correction and decoding efficiency.更多还原