Path Metric Range Based Iterative Construction Method for Polar Codes

In this paper, we consider the construction of polar codes for the successive cancellation list (SCL) decoding and propose a path metric range (PMR) based iterative construction method. In order to find the construction sequence for the SCL decoding, we simulate and calculate the PMRs and log-likelihood ratios (LLRs) of sub-channels to select the frozen bits and information bits, which is different from the the construction based on the successive cancellation (SC) decoding to calculate the error probability of sub-channels. The proposed construction can achieve 0.3 dB and 1.2 dB gain over the union-Bhattacharyya bound weight (SUBW) method and the Gaussian approximation (GA) method/polarization weight (PW) method in the SCL decoding algorithm, respectively. When using the CRC-aided SCL (CA-SCL) decoding, the proposed construction can also achieve 0.5 dB gain compared to traditional construction schemes.