Ergodic theory meets polarization II: A foundation of polarization theory for MACs
Ergodic theory meets polarization II: A foundation of polarization theory for MACs
复制标题
遍历理论与极化 II：MAC 极化理论的基础
DOI：
10.1109/isit.2015.7282896
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Rajai Nasser
中科院分区：
文献类型：
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作者：
Rajai Nasser
极化理论中的一个公开问题是确定在Arıkan风格的多址信道（MAC）结构中使用时总是导致极化的二元运算。本文通过给出二元运算序列是极化的一个充要条件来解决这个问题。我们证明了一个二元操作序列是MAC极化的当且仅当序列中每个二元操作的逆是强遍历的。推广了二元运算的遍历理论，研究了二元运算的乘积及其稳定划分的结构。证明了二元运算序列的乘积是强遍历的当且仅当序列中的所有运算都是强遍历的。
An open problem in polarization theory is to determine the binary operations that always lead to polarization when they are used in Arıkan style constructions for multiple access channels (MAC). This paper solves this problem by providing a necessary and sufficient condition for a sequence of binary operations to be polarizing. We show that a sequence of binary operations is MAC-polarizing if and only if the inverse of each binary operation in the sequence is strongly ergodic. We extend the ergodic theory of binary operations and study the products of binary operations and the structure of their stable partitions. We show that the product of a sequence of binary operations is strongly ergodic if and only if all the operations in the sequence are strongly ergodic.