This paper proposes new polar code design principles for the low-latency automorphism ensemble (AE) decoding. Our proposal permits to design a polar code with the desired automorphism group (if possible) while assuring the decreasing monomial property. Moreover, we prove that some automorphisms are redundant under AE decoding, and we propose a new automorphisms classification based on equivalence classes. Finally, we propose an automorphism selection heuristic based on drawing only one element of each class; we show that this method enhances the block error rate (BLER) performance of short polar codes even with a limited number of automorphisms.
翻译:本文为低纬度自成一体( AE) 共解码提出了新的极地代码设计原则。 我们的提案允许与理想的自成一体( 可能的话) 组设计极地代码, 同时确保单体财产的减少。 此外, 我们证明一些自成一体( AE) 解码( AE 解码) 下有些自成一体( ) 是多余的, 我们基于等同等级提出新的自成一体( II) 分类 。 最后, 我们基于每类只抽取一个元素, 提议自成一体选择超常; 我们表明, 这种方法可以提高极地短代码的区块误率( BLER ), 即使有数量有限的自成一体的自成一体( COLOBR ) 。