Design of Polar Codes with Puncturing and Extending

Abstract

This work proposes a novel polar code design scheme using puncturing and extending aiming to improve the successive cancellation list decoding (SCLD) performance. The proposed code design is conducted with Reed-Muller (RM) codes called \emph{base} codes. For a base code, puncturing is first performed to gain a degree of freedom, called \emph{transmission holes}. To this end, we develop a puncturing scheme minimizing the loss in the minimum distance of the base code. Then, we propose a novel extending scheme to produce additional bits which are transmitted through the transmission holes without rate loss. The extending scheme repeats some coded bits and/or intermediate bits induced during the encoding of base code. The repeated bits are decided in such a way to maximize the SCLD performance by utilizing reinforcement learning (RL). Moreover, we introduce a novel idea to reduce the learning space of RL, which greatly expedites the design of extended bits. While the proposed design scheme assumes RM codes as base codes, we show that it can be applied to various types of polar code. Simulation results show that the polar codes designed with the proposed scheme have notably improved SCLD performance compared to existing polar code designs.