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In this paper, we focus on the construction methods based MWD for polar codesto improve the performance with successive cancellation list (SCL) decoding. Wefirst propose an ordered and nested reliability sequence, namely MWD sequence,to improve the ML performance of polar codes and apply fast constructionwithout the original channel information. In the MWD sequence, the syntheticchannels are sorted by the partial MWD which is used to evaluate the influenceof information bit on MWD and we prove the MWD sequence is the optimum sequenceunder ML decoding. Then, since the list size of SCL decoding is limited, weintroduce an entropy constraint to establish a relationship between the listsize and the ML performance and propose a heuristic and greedy constructionmethod named bit grouping reorder based MWD (BGR-MWD) algorithm. In thealgorithm, we divide the synthetic channels into groups by the partial MWD andgreedily reorder the synthetic channels in some groups until the entropyconstraint is satisfied. The simulation results show the MWD sequence issuitable for constructing polar codes with short code length. Meanwhile, theBGR-MWD algorithm has superior performance over the traditional constructionmethods for long code length.

Construction Methods Based Minimum Weight Distribution for Polar Codes with Successive Cancellation List Decoding