Towards optimum cost in multi-hop networks with arbitrary network demands

This paper considers the problem of minimizing the communication cost for a general multi-hop network with correlated sources and multiple sinks. For the single sink scenario, it has been shown that this problem can be decoupled, without loss of optimality, into two separate subproblems of distributed source coding and finding the optimal routing (transmission structure). It has further been established that, under certain assumptions, such decoupling also applies in the general case of multiple sinks and arbitrary network demands. We show that these assumptions are significantly restrictive, and further provide examples to substantiate the loss, including settings where removing the assumptions yields unbounded performance gains. Finally, an approach to solving the unconstrained problem, where routing and coding cannot be decoupled, is derived based on Han and Kobayashi´s achievability region for multi-terminal coding.