Classification of Automorphisms for the Decoding of Polar Codes

TL;DR

This paper introduces new design principles for polar codes tailored for low-latency automorphism ensemble decoding, including automorphism classification and selection heuristics that improve error performance.

Contribution

It develops a novel automorphism classification and a heuristic for automorphism selection, enhancing polar code decoding efficiency and performance.

Findings

Automorphism classification based on equivalence classes.

Automorphism selection heuristic improves BLER.

Design principles enable desired automorphism groups.

Abstract

This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar code with the desired automorphism group (if possible) while assuring the decreasing monomial property. Moreover, we prove that some automorphisms are redundant under AE decoding, and we propose a new automorphisms classification based on equivalence classes. Finally, we propose an automorphism selection heuristic based on drawing only one element of each class; we show that this method enhances the block error rate (BLER) performance of short polar codes even with a limited number of automorphisms.