Classification of Automorphisms for the Decoding of Polar Codes

Charles Pillet (1, 2, 3) , Valerio Bioglio (1) , Ingmar Land (1)

1 Huawei Technologies France
2 IMT Atlantique - MEE - Département Mathematical and Electrical Engineering
3 Lab-STICC_COSYDE - Equipe Communication System Design

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.

Mots clés: Polar codes; code automorphism; successive cancellation; list decoding; permutation decoding; code design

Domaines: Informatique [cs]

Charles Pillet, Valerio Bioglio, Ingmar Land. Classification of Automorphisms for the Decoding of Polar Codes. IEEE International Conference on Communications (ICC), May 2022, Seoul, South Korea. ⟨10.1109/ICC45855.2022.9838937⟩. ⟨hal-03617270⟩