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

Performance Analysis for Polar Codes under Successive Cancellation List Decoding with Fixed List Size