Flow decomposition of cost-constrained networks
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In this thesis, we consider the problem of communicating data over a network of cost-constrained networks. We first look at a network with a single source and a single destination and prove that the information-theoretic cut-set outer bound matches the ow min-cut bound if the network has mutually independent, memoryless links. We then impose the cost constraint on the links and the overall network and prove that the aforementioned two bounds match in the limit as the packet size tends to infinity. We also provide transmission schemes that achieve the outer bounds, proving that these bounds actually equal the capacity of the network under the cost constraints. Finally, we consider a multi-source, multi-destination network of cost-constrained links and show that the information theoretic cut-set outer bound matches the ow outer bound, when the network is comprised of mutually independent, memoryless links.