Nested Symmetric Polar Codes

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.

6 pages, 2 figures. Presented at ICC 2025

References in corpus (4)

• Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations
• Algebraic Properties of Polar Codes From a New Polynomial Formalism
• On the Distribution of Partially Symmetric Codes for Automorphism Ensemble Decoding
• Shortened Polar Codes under Automorphism Ensemble Decoding