Bounds for network information flow with correlated sources

In the authors derived an outer bound, called functional dependence bound, for network information flow with independent sources. In this work, we derive outer bounds for network information flow with correlated sources and establish that the functional dependence bound is an outer bound for achievable region for networks with correlated sources. We also show that the bounds are loose and can be tightened by introducing auxiliary random variables describing structural correlation between source random variables. Finally, we discuss an important practical problem of constructing such auxiliary random variables given correlated source random variables.