Rate-Compatible Shortened PAC Codes

Rate matching techniques, such as puncturing and shortening, have been developed for polar codes to accommodate the specific code length requirements in practical applications. However, the existing shortening techniques cannot be directly applied to polarization-adjusted convolutional (PAC) codes. In this work, we propose an approach to shorten PAC codes by imposing constraints on the precoding process based on the shortening patterns. The proposed technique leads to up to 0.2 dB power gain in the error correction performance compared to shortened polar codes. This power gain can be further improved up to 0.45 dB by employing Reed-Muller (RM) polar rate profile based on the 5G universal reliability sequence. Furthermore, we shed light on these improvements by analysing the intersection of the shortening pattern and the GN-row decomposition of minimum weight codewords and its impact on the formation of these codewords, and evaluation of the error coefficients of the shortened codes versus their performance.