Weighted sum-rate functional dependence bound for network coding capacity

Explicit characterization of network coding capacity for multi-source multi-sink networks is an extremely hard problem. The linear programming bound is an explicit outer bound on network coding capacity but it is computationally very intensive. An edge-cut bound called functional dependence bound is an easily computable relaxation of the linear programming bound. However, the functional dependence bound is still very loose, even for two source unicast networks. In this paper, we characterize a set of Shannon-type inequalities for a given network that leads to new weighted bounds providing strict improvement over the functional dependence bound.