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The Complete SC-invariant Affine Automorphisms of Polar Codes

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 lower-triangular structure of transformation matrices to identify SC-invariant automorphisms. Furthermore, we provide an algorithm to determine the complete SC-invariant affine automorphisms under a specific polar code construction.

preprint2022arXivOpen access
Zicheng YeYuan LiHuazi ZhangRong LiJun WangGuiying YanZhiming Ma
math.ITInformation Theory
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Open access7 authors2 topics
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Zicheng YeYuan LiHuazi ZhangRong LiJun WangGuiying YanZhiming Ma

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