We revisit the primitive relay channel, introduced by Cover in 1987. Recent work derived upper bounds on the capacity of this channel that are tighter than the classical cutset bound using the concentration of measure. In this paper, we recover, generalize, and improve upon some of these upper bounds with simpler proofs using reverse hypercontractivity. To our knowledge, this is the first application of reverse hypercontractivity in proving first-order converses in network information theory.

中文翻译：

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通过反向超收缩性的中继通道的容量上限


我们重新审视了 Cover 于 1987 年引入的原始中继通道。最近的工作得出了该通道容量的上限，该上限比使用测度浓度的经典割集界限更紧。在本文中，我们使用反向超收缩性通过更简单的证明来恢复、概括和改进其中一些上限。据我们所知，这是逆超收缩性在证明网络信息论中的一阶逆过程中的首次应用。