On Evaluation of Interpolation Between Reed-Muller and Polar Rate-Profiling in PAC Codes

In this paper, we apply an interpolation method between Reed-Muller and polar codes to investigate rate profiling for Polarization-Adjusted Convolutional (PAC) codes over the Gaussian channel at short block lengths. We evaluate a normalized compression factor to quantity the transmission efficiency of information bits for the interpolated schemes. We propose a Signal-to-Noise Ratio (SNR)-based convolutional precoding to achieve a better protection of information bits depending on the channel conditions. In the experimental part, we evaluate the new rate-profiles in compliance with the SNR-based convolutional precoding by means of sequential stack decoder and demonstrate performance-computational complexity trade-offs valuable for practical usage of PAC codes. The new optimized code with e.g. interpolated parameter equal to 0.3 brings around 50 percent of gain in terms of block error rate at high SNR values along with a slight reduction in a number of paths in stack decoder compared with a Reed-Muller baseline rate-profile.