  In this paper, we extend the information theoretic framework that was
developed in earlier work to multi-hop network settings. For a given network,
we construct a novel deterministic model that quantifies the ability of the
network in transmitting private and common messages across users. Based on this
model, we formulate a linear optimization problem that explores the throughput
of a multi-layer network, thereby offering the optimal strategy as to what kind
of common messages should be generated in the network to maximize the
throughput. With this deterministic model, we also investigate the role of
feedback for multi-layer networks, from which we identify a variety of
scenarios in which feedback can improve transmission efficiency. Our results
provide fundamental guidelines as to how to coordinate cooperation between
users to enable efficient information exchanges across them.
