On the Distribution of Partially Symmetric Codes for Automorphism Ensemble Decoding
arXiv:2205.04338 · doi:10.1109/ITW55543.2023.10161664
Abstract
Automorphism Ensemble (AE) decoding has recently drawn attention as a possible alternative to list decoding of polar codes. In this letter, we investigate the distribution of Partially-Symmetric Reed-Muller (PS-RM) codes, a family of polar codes yielding good performances under AE decoding. We prove the existence of these codes for almost all code dimensions for code lengths . Moreover, we analyze the absorption group of this family of codes under SC decoding, proving that valuable permutations in AE decoding always exist. Finally, we experimentally show that PS-RM codes can outperform state-of-the-art polar-code-construction algorithms in terms of error-correction performance for short code lengths, while reducing decoding latency.
6 pages, 4 figures, 4 sub-figures, to be presented at IEEE Information Theory Workshop 2023