Deep Q-Learning Based Rate-Profile Design for Polarization Adjusted Convolutional (PAC) Codes

This paper introduces a novel rate-profile design for Polarization-Adjusted Convolutional (PAC) codes by simplifying the construction of an information set (inf set) for a PAC code of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> into the design of inf sets for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> component codes of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\frac{N}{M}$</tex>. We define a Markov Decision Process (MDP) that formulates the task of identifying the inf set that minimizes the Block Error Rate (BLER). To achieve this, we employ a Deep QNetwork (DQN) with an experience replay buffer to determine the optimal inf set with the lowest BLER. Simulation results demonstrate that under Successive Cancellation List (SCL) decoding, our designed PAC codes improve BLER compared to state-of-the-art PAC codes. This method is not limited to the design of PAC code inf set; it is applicable to inf set design for the general family of precoded Polar codes and supports any decoder.