Information Set Optimization of Polar Codes Under BP Decoder Based on Union Bound

One of the possible methods for obtaining reduced latency is the use of belief propagation (BP) decoding on polar codes. We proposed an iterative approach to get the information set optimal for BP decoding in order to mitigate performance degradation caused by BP decoding. In order to estimate the block error rate (BLER) of the BP decoding, we employ the union bound. Specifically, an all-zero codeword is transmitted through a low-noise channel, and it is decoded by successive cancellation list decoder with a large list size to capture low-weight codewords. By employing the proposed iterative algorithm, the performance were improved compared to the performance employing the information set optimized for the successive cancellation decoding.