Recently, a permutation-based successive cancellation (PSC) decoding framework for polar codes attaches much attention. It decodes several permuted codewords with independent successive cancellation (SC) decoders. Its latency thus can be reduced to that of SC decoding. However, the PSC framework is ineffective for permutations falling into the lower-triangular affine (LTA) automorphism group, as they are invariant under SC decoding. As such, a larger block lower-triangular affine (BLTA) group that contains SC-variant permutations was discovered for decreasing polar codes. But it was unknown whether BLTA equals the complete automorphism group. In this paper, we prove that BLTA equals the complete automorphisms of decreasing polar codes that can be formulated as affine trasformations.

翻译：最近,基于变异的相继取消极地代码解码框架(PSC)引起了很大的注意。 它用独立的相继取消解码器解码了几部变异的编码词。 因此,它的长度可以降为SC解码。 但是, PSC框架对于进入低边形自成一体(LTA)自成一体的变异组合来说是无效的,因为它们在SC解码中是无变的。 因此, 发现了一个含有 SC- 变异的极地代码的较大块的低端方形(BLTA) 组。 但不清楚 BLTA 是否等于完整的自成形组合。 在本文中, 我们证明 BLTA 等于可以作为裂变形组合而形成的减少的极地代码的完全自成形。