A Recursive Puncturing Method for PAC Codes Based on the Partial Order

The development of polarization-adjusted convolutional (PAC) codes has introduced a class of efficient designs for short packet transmission. In this contribution, aiming at more flexible code length and rate matching for time-varying channel scenarios, a low-complexity puncturing algorithm for PAC codes is proposed. Specifically, we introduce a Gaussian approximation (GA) algorithm for PAC codes and propose a GA-based optimization method for punctured patterns. Building on this, we present a Gaussian inverse mapping method based on partial order, utilizing a recursive approach to construct the initial set, which significantly reduces the search complexity. Subsequently, we develop a recursive puncturing algorithm based on partial order. Finally, we integrate this method with Reed-Muller (RM) rules, further reducing the complexity.