On the Distribution of Partially Symmetric Codes for Automorphism Ensemble Decoding

Permutation list decoding recently draws attention as a possible alternative for list decoding of polar codes. In this letter, we investigate the distribution of Reed-Muller partially symmetric codes (RM-PSC), a family of polar codes yielding good performances under permutation list decoding. We prove the existence of these codes for almost all code dimensions if the code length is not greater than 256. Moreover, we analyze the absorption group of this family of codes under SC decoding, showing that it may include one or more blocks of size larger than one. Finally, we show by simulations that RM-PSC can outperform state-of-the-art polar codes constructions in terms of error correcting performance for short code lengths, while reducing decoding latency.