Designing Polarization-Adjusted Convolutional (PAC) Codes with Rate Matching

In this paper, we propose a convolution transform design for polarization-adjusted convolutional (PAC) codes with rate matching. The proposed convolution transform is adapted to rate matching patterns. More specifically, bits output from rate profiling but with indices punctured (or shortened) in rate matching do not participate in convolution. Also, the forward convolution transform is extended to the general convolution transform. It is shown that recursive feedback convolution can perform better than the original forward convolution. Simulation results show that PAC codes with the proposed design can perform about $0.1\sim 0.2\mathrm{dB}$ better than 5G polar codes at a block error rate of $10^{-4}$.