The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

翻译：代码的自定义组是将整个代码映射到它的代码符号的一组。 对于极地代码,仅知道自定义组的一部分,即仅以该代码合成通道的部分顺序为基础。然而,根据设计,极地代码可以拥有更丰富的自定义组。在本文中,我们将长期协议扩展至一般同系群(GA)的一个较大的分组,即区块低三角同系群(BLTA),并显示它包含在极地代码的自定义组中。此外,我们提供了一个低复杂度的算法,用于为给定的信息/冻分集寻找该组并确定其大小。最重要的是,我们将这些结果应用于基于自定义的极地代码解码中,并报告类似的错误率表现与相近的取消列表(SCL)解码的相近。