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：本文聚焦于基于最小权值分布（MWD）的极化码构造方法，旨在提升连续消除列表（SCL）译码的性能。我们首先提出一种有序且嵌套的可靠性序列，即MWD序列，以改善极化码的最大似然（ML）性能，并实现无需原始信道信息的快速构造。在MWD序列中，合成信道按照部分MWD进行排序，该部分MWD用于评估信息比特对MWD的影响，且我们证明了在ML译码下MWD序列为最优序列。进一步，由于SCL译码的列表大小受限，我们引入熵约束以建立列表大小与ML性能之间的关系，并提出一种启发式贪心构造算法——基于比特分组重排的MWD（BGR-MWD）算法。该算法通过部分MWD将合成信道划分为若干组，并贪心地重排组内合成信道，直至满足熵约束条件。仿真结果表明，MWD序列适用于短码长极化码的构造；同时，对于长码长场景，BGR-MWD算法的性能优于传统构造方法。