On optimum communication cost for joint compression and dispersive information routing

In this paper, we consider the problem of minimum cost joint compression and routing for networks with multiple-sinks and correlated sources. We introduce a routing paradigm, called dispersive information routing, wherein the intermediate nodes are allowed to forward a subset of the received bits on subsequent paths. This paradigm opens up a rich class of research problems which focus on the interplay between encoding and routing in a network. What makes it particularly interesting is the challenge in encoding sources such that, exactly the required information is routed to each sink, to reconstruct the sources they are interested in. We demonstrate using simple examples that our approach offers better asymptotic performance than conventional routing techniques. We also introduce a variant of the well known random binning technique, called `power binning´, to encode and decode sources that are dispersively transmitted, and which asymptotically achieves the minimum communication cost within this routing paradigm.