On the Polarization Levels of Automorphic-Symmetric Channels
On the Polarization Levels of Automorphic-Symmetric Channels
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关于自守对称信道的偏振能级
DOI：
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发表时间：
2018
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通讯作者：
Rajai Nasser
中科院分区：
文献类型：
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作者：
Rajai Nasser
众所周知，如果阿贝尔群运算被用于Arıkan风格的构造中，则会发生多级极化。极化理论中的一个开放问题是确定给定信道的极化水平。在本文中，我们讨论的极化水平的一个家庭的信道，我们称之为自同构对称信道。我们证明了自同构对称信道的极化能级是由特征子群决定的。特别地，如果所使用的组不包含任何非平凡的特征子群，则对于几乎完美和几乎无用的信道，我们只有两级极化。
It is known that if an Abelian group operation is used in an Arıkan-style construction, multilevel polarization occurs. An open problem in polarization theory is to determine the polarization levels of a given channel. In this paper, we discuss the polarization levels of a family of channels that we call automorphic-symmetric channels. We show that the polarization levels of an automorphic-symmetric channel are determined by characteristic subgroups. In particular, if the group that is used does not contain any non-trivial characteristic subgroup, we only have two-level polarization to almost perfect and almost useless channels.