Classification of Automorphisms for the Decoding of Polar Codes

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.