Improve Polar/PAC Codes via Efficient Estimation on Weight Distribution

In this paper, we first introduce an efficient method for estimating weight distributions of polar codes and polarization-adjusted convolutional (PAC) codes. Based on a recursive algorithm of computing the weight enumerating functions of polar cosets, this method focuses on two key objectives: accurately determining the number of low-weight codewords and quickly approximating the distribution of high-weight codewords. Then we optimize the Reed Muller-Gaussian Approximation (RM-GA) rate profiling scheme with the help of the proposed method aiming at reducing the truncated union bound (TUB). Simulation results demonstrate that the proposed hybrid method maintains competitively low complexity while effectively achieving the objectives. The TUB-improved RM-GA rate profiling scheme for polar codes exhibits a performance improvement of nearly 1 dB at 10
^–4
compared to GA and around 0.3 dB improvement compared to RM-GA. The proposed scheme for PAC codes also achieves an enhancement of approximately 0.52 dB at 10
^–5
compared to the commonly used RM-GA scheme.