LDPC码短环的置信传播改进算法

Belief Propagation Improvement Algorithm for LDPC Codes with Short Cycles

摘要: 低密度奇偶校验码(Low Density Parity Check Codes, LDPC codes)具有高效译码性能，列入了5GNR标准，在实际通信中被广泛使用。LDPC码的校验矩阵与Tanner图具有一一对应关系，当LDPC码对应的Tanner图是树时，置信传播算法译码结果等价于最大似然译码结果。但在实际应用中，LDPC码的Tanner图包含大量短环，运用置信传播算法时短环的存在会导致信息重复计算造成计算误差，其中四环的影响最为明显。为此大量学者研究寻找提高译码性能的改进算法，提出以牺牲计算量为代价降低或解决短环内信息传递的误差。为了解决短环问题，在工程中能得到更好的应用，本文在置信传播算法上做了改进，提出了改进的对数域置信传播算法，使其不损失原算法的译码性能，保证具有四环的Tanner图信息传递具有良好性能，并降低了置信传播译码算法的计算复杂度。

Abstract: Low Density Parity Check Codes have high decoding performance and are included in the 5GNR standard, which is widely used in practical communication. The check matrix of LDPC codes has a one-to-one correspondence with the Tanner graph, and when the Tanner graph of LDPC codes is a tree, the decoding result of the belief propagation algorithm is equivalent to the maximum likeli-hood decoding result. However, in practice, the Tanner graph of LDPC codes contains a large number of short cycles, and the existence of short cycles in the belief propagation algorithm will lead to computational errors caused by double computation of information, among which the impact of four-cycle is most obvious. For this reason, a large number of scholars have researched to find im-proved algorithms to improve the decoding performance and reduce or solve the error of infor-mation transmission in short cycles at the expense of computation. In order to solve the short-cycle problem and get better application in engineering, this paper makes improvements on the belief propagation algorithm and proposes an improved log-domain belief propagation algorithm so that it does not lose the decoding performance of the original algorithm, ensures good performance of the Tanner graph information transfer with four-cycle, and reduces the computational complexity of the belief propagation decoding algorithm.