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It has been shown that there is a duality between the linear network coding solution and the entropic vectors induced by collection of subspaces in a vector space over a finite field (dubbed linearly constructed entropic vectors). The region of all linearly constructed vectors, coincides with the set of all representable polymatroids. For any integer polymatroid, there is an associated matroid, which...
An explicit characterization of the capacity region of the general network coding problem is one of the best known open problems in information theory. A simple set of bounds that is often used in the literature to show that certain rate tuples are infeasible are based on the graph-theoretic notion of cut. The standard cut-set bounds, however, are known to be loose in general when there are multiple...
This paper considers classical networks with collocated multicast messages and more than three sink nodes. A new class of information-theoretic upper bounds on the achievable rates is established, generalizing the standard cut-set bounds. These new bounds involve three basic cuts of the network and are established only via the submodularity of the entropy function.
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