Polar coding solutions demonstrate excellent performance under the list decoding that is challenging to implement in hardware due to the path sorting operations. As a potential solution to this problem, permutation decoding recently became a hot research topic. However, it imposes more constraints on the code structure. In this paper, we study the structural properties of Arikan's polar codes. It is known that they are invariant under lower-triangular affine permutations among others. However, those permutations are not useful in the context of permutation decoding. We show that, unfortunately, the group of affine automorphisms of Arikan's polar codes asymptotically cannot be much bigger than the group of lower-triangular permutations.
翻译:极地编码解决方案显示,由于路径分解操作,在硬件中执行的解码程序有挑战性。 作为这一问题的潜在解决办法,变异编码最近成为了热研究课题。 但是,它给代码结构带来了更多的限制。 在本文中,我们研究了Arikan的极地代码的结构特性。众所周知,这些代码在较低边距的边距变异中是无变的。然而,这些变异在变异解解码方面没有用处。我们表明,不幸的是,Arikan的极地代码的直系自成形学群不会比低边形变异组大得多。