Polarization-adjusted convolutional (PAC) codes are a new family of linear block codes that can perform close to the theoretical bounds in the short block-length regime. These codes combine polar coding and convolutional coding. In this study, we show that PAC codes are equivalent to a new class of codes consisting of inner cyclic codes and outer polar- and Reed-Muller-like codes. We leverage the properties of cyclic codes to establish that PAC codes outperform polar- and Reed-Muller-like codes in terms of minimum distance.

翻译：极化调整卷积（PAC）码是一类新型线性分组码，在短码长范围内能够接近理论极限。此类码结合了极化编码与卷积编码。本研究表明，PAC码等价于由内循环码与外类极化码和里德-穆勒码构成的新类型码。我们利用循环码的性质论证了PAC码在最小距离方面优于类极化码和里德-穆勒码。