A Heuristic Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) codes

In this paper, we propose a heuristic algorithm for rate-profile construction of Arikan's Polarization Assisted Convolutional (PAC) codes. This method can be used for any blocklength, rate and convolutional precoding polynomial. The proposed algorithm tries to create a rate-profile for which the corresponding PAC code is, in a sense, locally optimized for having maximum possible minimum distance.

Simulation results show that PAC codes constructed with the proposed algorithm perform better in terms of frame erasure rate (FER) compared to the PAC codes constructed with rate profiling designs in existing literature for various list lengths. Further, by using a (64, 32) PAC code as an example, it is shown that the choice of convolutional precoding polynomial can have a significant impact on FER performance. Finally, we demonstrate that for a target FER of $\mathbf{10^{-5}}$, (128, 72) PAC codes constructed with our proposed algorithm is just 0.35 dB away from the information theoretic limit at this blocklength.