Design of Compactly Specified Polar Codes With Dynamic Frozen Bits Based on Reinforcement Learning

This paper focuses on the design of high-performance polar codes with dynamic frozen bits that can be compactly specified. We split the code design problem into the frozen set design and the frozen bit expression design problems. To solve the first problem, we analyze the connection between the code minimum distance and the frozen set. This analysis leads to a novel frozen set structure that ensures a low frame error rate (FER) under successive cancellation list (SCL) decoding. Given a bit-channel reliability sequence, our frozen set structure reduces the problem of frozen set design to that of selecting three integer numbers. We develop a reinforcement learning technique to find the values of these integer numbers minimizing the FER under SCL decoding. We then propose a simple deterministic method producing efficient expressions for dynamic frozen bits. Simulation results show that the proposed compactly-specified polar codes of lengths 512 to 4096 outperform the state-of-the-art polar code constructions under SCL decoding in the high SNR regime.