  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.
