A Modified Q-Learning Algorithm for Rate-Profiling of Polarization Adjusted Convolutional (PAC) Codes

TL;DR

A reinforcement learning based algorithm for rate-profile construction of Arikan’s Polarization Adjusted Convolutional (PAC) codes is proposed and a set of new reward and update strategies are presented which help the reinforcement learning agent discover much better rate-profiles than those present in existing literature.

Abstract

In this paper, we propose a reinforcement learning based algorithm for rate-profile construction of Arikan's Polarization Assisted Convolutional (PAC) codes. This method can be used for any blocklength, rate, list size under successive cancellation list (SCL) decoding and convolutional precoding polynomial. To the best of our knowledge, we present, for the first time, a set of new reward and update strategies which help the reinforcement learning agent discover much better rate-profiles than those present in existing literature. Simulation results show that PAC codes constructed with the proposed algorithm perform better in terms of frame erasure rate (FER) compared to the PAC codes constructed with contemporary rate profiling designs for various list lengths. Further, by using a (64, 32) PAC code as an example, it is shown that the choice of convolutional precoding polynomial can have a significant impact on rate-profile construction of PAC codes.

Figures (7)

• Figure 1: FER Performance of (128, 64) polar code variants
• Figure 2: Coding scheme of PAC code
• Figure 3: FER performance of $(64, 32)$ CRC-Aided polar code and PAC code variants with $\mathbf{w}=[1,0,1,1,0,1,1]$ under SCL decoding with $L=8$.
• Figure 4: FER performance of $(64, 32)$ polar code, CRC-Aided polar code and PAC code variants with $\mathbf{w}=[1,0,1,1,0,1,1]$ under SCL decoding with $L=32$.
• Figure 5: FER performance of $(128, 72)$ polar code and PAC code variants with $\mathbf{w}=[1,0,1,1,0,1,1]$ under SCL decoding with $L=8$.