随机信道的渐近容量

Tobias Sutter, David Sutter, J. Lygeros
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引用次数: 1

摘要

我们考虑离散无记忆信道的输入和输出字母大小为n通道转移矩阵的条目包括独立且同分布根据一些概率分布v (R≥0,B (R≥0))在标准化之前,v在哪里,E (X日志)2 1 1:= E (X)和μ2:= E (X日志)与分布随机变量X诉我们证明极限n→∞,这样一个信道的容量收敛于日志μμ2 /μ1 - 1几乎肯定在L2。我们进一步证明了这些随机信道的容量在n上指数收敛于这个渐近值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic capacity of a random channel
We consider discrete memoryless channels with input and output alphabet size n whose channel transition matrix consists of entries that are independent and identically distributed according to some probability distribution v on (R≥0, B(R≥0)) before being normalized, where v is such that E[X log X)2 1 <; ∞, μ1 := E[X] and μ2 := E[X log X] for a random variable X with distribution v. We prove that in the limit as n → ∞, the capacity of such a channel converges to μ21 - log μ1 almost surely and in L2. We further show that the capacity of these random channels converges to this asymptotic value exponentially in n.
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