Path Metric Range and LLR-Based Design of Polar Codes and PAC Codes for SCL Decoding

Polar codes and polarization-adjusted convolutional (PAC) codes can achieve good performance with successive cancellation list (SCL) decoding. When constructed by the Reed-Muller rate profile, the rate of PAC code is limited, and its performance is not competitive for large block lengths under the SCL decoder with small or modest list sizes. How to design optimal polar codes and PAC codes for SCL decoding are still open problems. In this letter, we analyse the probability of the correct path in the list according to the path metric in SCL decoding. We calculate the path metric range and log-likelihood ratio of each sub-channel. Then we select the frozen bits to maximize the probability of the correct path in the list. Simulation results show that the proposed polar codes and PAC codes have better performance compared with other advanced constructions at a wide range of code rates and block lengths.