自动变形的极极代码共解码 (Polar Codes for Automorphism Ensemble Decoding)

In this paper we deal with polar code automorphisms that are beneficial under low-latency automorphism ensemble (AE) decoding, and we propose polar code designs that have such automorphisms. Successive-cancellation (SC) decoding and thus SC-based AE decoding are invariant with respect to the only known polar code automorphisms, namely those of the lower-triangular affine (LTA) group. To overcome this problem, we provide methods to determine whether a given polar code has non-LTA automorphisms and to identify such automorphisms. Building on this, we design specific polar codes that admit automorphisms in the upper-diagonal linear (UTL) group, and thus render SC-based AE decoding effective. Demonstrated by examples, these new polar codes under AE decoding outperform conventional polar codes under SC list decoding in terms of error rate, while keeping the latency comparable to SC decoding. Moreover, state-of-the-art BP-based permutation decoding for polar codes is beaten by BP-based AE thanks to this design.

翻译：在本文中,我们处理在低纬度自成一体(AE)共解码(AE)下有益的极地代码自成一体(AE),我们提出具有这种自成一体的极地代码设计。相继的取消(SC)解码,从而基于SC的自成一体(AE)解码,对于已知的唯一极地代码自成一体(即低纬度三角形的LTA)组的自成一体(LTA),我们处理的是极地代码。为了克服这一问题,我们提供了一些方法,以确定给定的极地代码是否有非LTA自成一体(AE)的自成一体(AE),并查明这些自成一体的极地代码。在此基础上,我们设计了特定的极地代码,以允许上对角线(UTL)组的自成一体(SC)自成一体(AE),从而使得基于SC的自成一体(AE)解码有效。例如,AEED解码(LTAE)下的新极代码以误率解码(LTA)解码(LTATAD)组)的脱码(LT)中,同时保持悬界与SC解码的自成非自成一体(LTTAP-P-P-BP-B-B-B-B-B-B-B-B-B-B-B-B-C-C-D-D-D-de)的)的代码的脱码与极代码的脱码。此外制成的脱码被打破了。