An Information-Theoretic Perspective on Successive Cancellation List Decoding and Polar Code Design

TL;DR

This paper explores the information-theoretic aspects of successive cancellation list decoding for polar codes, providing bounds, estimation methods, and code modifications to enhance decoding performance over various channels.

Contribution

It introduces bounds and estimation techniques for list size in SCL decoding, and proposes code modifications to improve performance with practical list sizes.

Findings

Exemplary codes outperform 5G polar codes on BAWGN channels.

The required list size concentrates around its mean for large block lengths.

Efficient bounds and estimation methods for list size are developed.

Abstract

This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless symmetric (BMS) channels. It also provides upper and lower bounds for these quantities that can be computed efficiently for very long codes. For the binary erasure channel (BEC), we provide a simple method to estimate the mean accurately via density evolution. The analysis shows how to modify, e.g., Reed-Muller codes, to improve the performance when practical list sizes, e.g., $L\in[8, 1024]$, are adopted. Exemplary constructions with block lengths $N\in\{128,512\}$ outperform polar codes of 5G over the binary-input additive white Gaussian noise channel. It is further shown that there is a concentration around the mean of the logarithm of the required list size for sufficiently large block lengths, over discrete-output BMS channels. We provide the probability mass functions (p.m.f.s) of this logarithm, over the BEC, for a sequence of the modified RM codes with an increasing block length via simulations, which illustrate that the p.m.f.s concentrate around the estimated mean.