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.
翻译：极地代码自成一体共和(AE)解码建议,方法是通过相继取消(SC)解码符解码,对极地代码解码,从而与相继取消(SC)解码器解码相平行,比相继取消(SCL)解码器的解码法更低,然而,有些自成一体的共和(AE)解码法是多余的。在本文中,我们发现一个必要和充分的条件,涉及变异矩阵的区块低边形结构,以识别SC-异性自成形。此外,我们提供了一种算法,用以确定特定极地代码构造下的完全的SC-异性方形自成形。
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