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Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper, the authors introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that results in bounds that are tighter than the corresponding cut-set bounds. They also define the concept of "Uncertainty region" which might be of independent interest. They provide a full characterization of this region for the case of two correlated random variables. The bounding technique works as follows: on one hand they show that if the communication problem is solvable, the uncertainty of certain random variables in the network with respect to imaginary parties that have partial knowledge of the sources must satisfy some constraints that depend on the network architecture.
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