The Complete SC-Invariant Affine Automorphisms of Polar Codes (Guiying Yan, Zhiming Ma)

Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders in parallel and hence has lower latency compared to that of successive cancellation list (SCL) decoding. However, some automorphisms are SC-invariant, thus are redundant in AE decoding. In this paper, we find a necessary and sufficient condition related to the block lowertriangular structure of transformation matrices to identify SCinvariant automorphisms. Furthermore, we provide an algorithm to determine the complete SC-invariant affine automorphisms under a specific polar code construction.

Publication:

2022 IEEE International Symposium on Information Theory (ISIT), Espoo, Finland, 2022, pp. 2368-2373, doi: 10.1109/ISIT50566.2022.9834828.

Authors:

Zicheng Ye

University of Chinese Academy of Sciences; Academy of Mathematics and Systems Science

Yuan Li

University of Chinese Academy of Sciences; Academy of Mathematics and Systems Science; Huawei Technologies Co. Ltd.

Huazi Zhang

Huawei Technologies Co. Ltd.

Rong？Li

Huawei Technologies Co. Ltd.

Jun Wang

Huawei Technologies Co. Ltd.

Guiying Yan

University of Chinese Academy of Sciences; Academy of Mathematics and Systems Science

Email: yangy@amss.ac.cn

Zhiming Ma

University of Chinese Academy of Sciences; Academy of Mathematics and Systems Science

Email: mazm@amt.ac.cn