Polar Codes for Automorphism Ensemble Decoding

TL;DR

This paper introduces polar code designs with specific automorphisms that enhance low-latency automorphism ensemble decoding, outperforming traditional methods in error rate and decoding speed.

Contribution

It proposes methods to identify non-LTA automorphisms in polar codes and designs codes with UTL automorphisms to improve AE decoding performance.

Findings

New polar codes with UTL automorphisms outperform conventional codes under AE decoding.

AE decoding with these codes surpasses SC list decoding in error rate.

BP-based AE decoding exceeds state-of-the-art BP permutation decoding.

Abstract

In this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code automorphisms, namely those of the lower-triangular affine (LTA) group. To overcome this problem, we provide methods to determine whether a given polar code has non-LTA automorphisms and to identify such automorphisms. Building on this, we design specific polar codes that admit automorphisms in the upper-diagonal linear (UTL) group, and thus render SC-based AE decoding effective. Demonstrated by examples, these new polar codes under AE decoding outperform conventional polar codes under SC list decoding in terms of error rate, while keeping the latency comparable to SC decoding. Moreover, state-of-the-art BP-based permutation decoding for polar codes is beaten by BP-based AE thanks to this design.