论文标题
自动形态合奏解码的极地代码的组属性
Group Properties of Polar Codes for Automorphism Ensemble Decoding
论文作者
论文摘要
在本文中，我们提出了对极地代码的自动形态群体的分析，其设计范围的范围是针对自动形态集合（AE）解码的代码的范围。我们证明了减少单码代码的概念与对极地代码的描述的通用部分阶（UPO）框架之间的等效性。然后，我们分析了仿射自动形态的极地代码组的代数特性，提供了对其结构的新颖描述，并提出了对自动形态的分类，从而提供了相同的置换解码结果。最后，我们提出了一种方法，以列出所有可能导致AE解码下不同候选者的自动形态。通过介绍冗余自动形态的概念，我们发现在AE-SC下提供可能不同的代码字候选者的最大排列数量，提出了一种列出所有这些方法的方法。对极地代码解码的AE算法的误差校正性能的数值分析得出了论文。
In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble (AE) decoding. We prove the equivalence between the notion of decreasing monomial codes and the universal partial order (UPO) framework for the description of polar codes. Then, we analyze the algebraic properties of the affine automorphisms group of polar codes, providing a novel description of its structure and proposing a classification of automorphisms providing the same results under permutation decoding. Finally, we propose a method to list all the automorphisms that may lead to different candidates under AE decoding; by introducing the concept of redundant automorphisms, we find the maximum number of permutations providing possibly different codeword candidates under AE-SC, proposing a method to list all of them. A numerical analysis of the error correction performance of AE algorithm for the decoding of polar codes concludes the paper.
