Comparison of Channels: Criteria for Domination by a Symmetric Channel
Comparison of Channels: Criteria for Domination by a Symmetric Channel
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渠道比较：对称渠道统治的标准
DOI：
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发表时间：
2016
影响因子：
2.5
通讯作者：
Yury Polyanskiy
中科院分区：
文献类型：
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作者：
A. Makur;Yury Polyanskiy
本文研究的基本问题，是否一个给定的通道<inline-formula><tex-math notation="LaTeX">V$</tex-math></inline-formula>可以占主导地位（在精确的意义上更嘈杂）由一个<inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>元对称通道。信道之间的低噪声关系的概念起源于网络信息理论（广播信道），并根据互信息或Kullback-Leibler散度定义。我们提供了一个等价的特征<inline-formula><tex-math notation="LaTeX">$χ ^{2}$</tex-math></inline-formula>-发散。此外，我们开发了一个简单的标准，由一个<inline-formula><tex-math notation="LaTeX">$q$</tex-math></inline-formula>-ary对称通道的随机矩阵定义的通道<inline-formula><tex-math notation="LaTeX">$V$的</tex-math></inline-formula>最小条目方面的支配。对于有限阿贝尔群上加性噪声信道的特殊情况，该准则得到了加强。最后，它表明，支配的对称通道意味着（通过比较狄利克雷形式）的对数Sobolev不等式的原始通道。
This paper studies the basic question of whether a given channel <inline-formula> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> can be dominated (in the precise sense of being more noisy) by a <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary symmetric channel. The concept of less noisy relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback–Leibler divergence. We provide an equivalent characterization in terms of <inline-formula> <tex-math notation="LaTeX">$chi ^{2}$ </tex-math></inline-formula>-divergence. Furthermore, we develop a simple criterion for domination by a <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel <inline-formula> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula>. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel.