Nested Symmetric Polar Codes

TL;DR

This paper introduces a data-driven method for designing flexible polar codes, particularly optimized for automorphism ensemble decoding, enhancing performance for URLLC and mMTC applications.

Contribution

It presents a novel algorithm for rate- and length-flexible polar code design and derives theoretical results on code nesting for improved decoding.

Findings

Outperforms existing AED code designs

Outperforms 5G polar codes under CRC-aided SCL decoding

Provides a fully nested, rate-compatible code sequence

Abstract

In this paper, we propose a data-driven algorithm to design rate- and length-flexible polar codes. While the algorithm is very general, a particularly appealing use case is the design of codes for automorphism ensemble decoding (AED), a promising decoding algorithm for ultra-reliable low-latency communications (URLLC) and massive machine-type communications (mMTC) applications. To this end, theoretic results on nesting of symmetric polar codes are derived, which give hope in finding a fully nested, rate-compatible sequence suitable for AED. Using the proposed algorithms, such a flexible polar code design for automorphism ensemble successive cancellation (SC) decoding is constructed, outperforming existing code designs for AED and also the 5G polar code under cyclic redundancy check (CRC)-aided successive cancellation list (SCL) decoding.