Trellis-Based Construction of Polar Codes for SCL Decoding

In this paper, we propose an approach to construction of polar codes for successive cancellation list (SCL) decoding with a preset list size. For a given code length, we construct a trellis through which a path corresponds to a polar code. Then, we employ a sequential search algorithm to find an expected path based on four path metrics and five path selection rules. Additionally, for polarization-adjusted convolutional (PAC) construction, we optimize the convolutional generator polynomial based on our constructed polar code. Numerical results show that our polar/PAC codes can achieve satisfactory performance.

I. Introduction

In 2009, Arikan proposed polar codes, marking a significant breakthrough in coding theory [1]. The polar codes possess a recursive structure, enabling encoding and decoding with low complexity. Crucially, it has been proved that polar codes can asymptotically achieve the capacity of any symmetric binary-input discrete memoryless channel (BI-DMC) as the code length increases. However, in the short-length regime, polar codes exhibit inferior error correction performance when compared with Bose-Chaudhuri-Hocquenghem (BCH) codes, Reed-Muller (RM) codes, low-density parity-check (LDPC) codes and turbo codes [2].