PROJECT TITLE :
Generalized Cut-Set Bounds for Broadcast Networks
An specific characterization of the capability region of the final network coding downside is one in every of the best known open problems in info theory. A simple set of bounds that is typically utilized in the literature to indicate that certain rate tuples are infeasible are based mostly on the graph-theoretic notion of cut. The standard cut-set bounds, however, are known to be loose generally when there are multiple messages to be communicated in the network. This paper focuses on broadcast networks, for which the standard cut-set bounds are closely connected to union as a particular set operation to mix completely different easy cuts of the network. A brand new set of express network coding bounds, that combine different straightforward cuts of the network via a selection of set operations (not simply the union), are established via their connections to extremal inequalities for submodular functions. The tightness of those bounds are demonstrated via applications to combination networks.
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