This paper considers a multimessage network where each node may send a message to any other node in the network. Under the discrete memoryless model, we prove the strong converse theorem for any network whose cut-set bound is tight, i.e., achievable. Our result implies that for any fixed rate vector that resides outside the capacity region, the average error probability of any sequence of length-n codes operated at the rate vector must tend to 1 as n approaches infinity. The proof is based on the method of types and is inspired by the work of Csiszár and Körner in 1982 which fully characterized the reliability function of any discrete memoryless channel with feedback for rates above capacity. In addition, we generalize the strong converse theorem to the Gaussian model where each node is subject to an almost-sure power constraint. Important consequences of our results are new strong converses for the Gaussian multiple access channel with feedback and the following relay channels under both models: the degraded relay channel (RC), the RC with orthogonal sender components, and the general RC with feedback.

中文翻译：

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具有紧密割集约束的多消息网络的强逆定理

本文考虑了一个多消息网络，其中每个节点都可以向网络中的任何其他节点发送消息。在离散无记忆模型下，我们证明了任何割集约束紧密（即可实现）的网络的强逆定理。我们的结果表明，对于任何固定的速率向量驻留在容量区域之外，长度-的任何序列的平均误差概率Ñ以速率向量操作代码必须趋向于1作为Ñ接近无限。该证明基于类型方法，并受到Csiszár和Körner在1982年的工作的启发，该工作充分表征了任何离散无记忆通道的可靠性功能，并具有高于容量的速率反馈。另外，我们将强逆定理推广到高斯模型，其中每个节点都受到几乎确定的幂约束。我们的结果的重要结果是，在两种模型下，带反馈的高斯多址访问信道和以下中继信道都发生了新的强烈反响：降级中继信道（RC），具有正交发送器分量的RC和具有反馈的常规RC。