  In this paper, we first indicate that the block error event of polar codes
under successive cancellation list (SCL) decoding is composed of path loss (PL)
error event and path selection (PS) error event, where the PL error event is
that correct codeword is lost during the SCL decoding and the PS error event is
that correct codeword is reserved in the decoded list but not selected as the
decoded codeword. Then, we simplify the PL error event by assuming the all-zero
codeword is transmitted and derive the probability lower bound via the joint
probability density of the log-likelihood ratios of information bits.
Meanwhile, the union bound calculated by the minimum weight distribution is
used to evaluate the probability of the PS error event. With the performance
analysis, we design a greedy bit-swapping (BS) algorithm to construct polar
codes by gradually swapping information bit and frozen bit to reduce the
performance lower bound of SCL decoding. The simulation results show that the
BLER performance of SCL decoding is close to the lower bound in the medium to
high signal-to-noise ratio region and we can optimize the lower bound to
improve the BLER performance of SCL decoding by the BS algorithm.
