In this paper, we focus on the construction methods based MWD for polar codes to improve the performance with successive cancellation list (SCL) decoding. We first propose an ordered and nested reliability sequence, namely MWD sequence, to improve the ML performance of polar codes and apply fast construction without the original channel information. In the MWD sequence, the synthetic channels are sorted by the partial MWD which is used to evaluate the influence of information bit on MWD and we prove the MWD sequence is the optimum sequence under ML decoding. Then, since the list size of SCL decoding is limited, we introduce an entropy constraint to establish a relationship between the list size and the ML performance and propose a heuristic and greedy construction method named bit grouping reorder based MWD (BGR-MWD) algorithm. In the algorithm, we divide the synthetic channels into groups by the partial MWD and greedily reorder the synthetic channels in some groups until the entropy constraint is satisfied. The simulation results show the MWD sequence is suitable for constructing polar codes with short code length. Meanwhile, the BGR-MWD algorithm has superior performance over the traditional construction methods for long code length.
翻译:本文针对极化码的最小重量分布(MWD)构造方法,结合连锁取消列表(SCL)解码方法,提出了基于构造方法的改进方案,以提高极化码的性能。首先提出了有序和嵌套的可靠性序列,即MWD序列,用于改进极化码的最大相似度(ML)性能,并且在不需要原始通道信息的情况下,应用了快速构造的方法。在MWD序列中,通过部分MWD对合成通道进行排序,以评估信息位对MWD的影响,并且证明MWD序列是ML解码的最优序列。随后,由于SCL解码的列表大小是有限制的,为建立列表大小与ML性能之间的关系,我们引入一个熵约束,并提出了一种基于位分组重新排序的MWD(BGR-MWD)算法。在该算法中,根据部分MWD将合成通道分成若干组,然后采用贪心算法对某些组内的合成通道进行重新排序,直到满足熵约束。仿真结果表明,MWD序列适用于构造短码长的极化码。与传统的构造方法相比,BGR-MWD算法在长码长时具有更优越的性能。