耦合干涉信道的逆界及Costa猜想的证明

Yury Polyanskiy, Yihong Wu
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引用次数: 2

摘要

证明了在适当的正则性条件下,微分熵是O(√n)-Lipschitz,是关于二次Wasserstein距离的概率分布的函数。在类似的条件下,(离散)香农熵在乘积空间的分布中相对于Ornstein's d -distance(对应于Hamming距离的Wasserstein距离)显示为O(n)-Lipschitz。这些结果与塔拉格兰德和马顿的传输信息不等式一起,允许人们用其i.i.d近似值代替未知的多用户干扰。作为应用,证明了双用户高斯干涉信道的一个新的外界,特别解决了Costa(1985)的“缺角点”问题。
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Converse bounds for interference channels via coupling and proof of Costa's conjecture
It is shown that under suitable regularity conditions, differential entropy is O(√n)-Lipschitz as a function of probability distributions on ℝn with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) Shannon entropy is shown to be O(n)-Lipschitz in distributions over the product space with respect to Ornstein's d̅-distance (Wasserstein distance corresponding to the Hamming distance). These results together with Talagrand's and Marton's transportation-information inequalities allow one to replace the unknown multi-user interference with its i.i.d. approximations. As an application, a new outer bound for the two-user Gaussian interference channel is proved, which, in particular, settles the “missing corner point” problem of Costa (1985).
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