Network Coding Capacity: A Functional Dependence Bound

Explicit characterization and computation of the multi-source network coding capacity region (or even bounds) is long standing open problem. In fact, finding the capacity region requires determination of the set of all entropic vectors ${\mathrm{\Gamma }}^{\ast }$, which is known to be an extremely hard problem. On the other hand, calculating the explicitly known linear programming bound is very hard in practice due to an exponential growth in complexity as a function of network size. We give a new, easily computable outer bound, based on characterization of all functional dependencies in networks. We also show that the proposed bound is tighter than some known bounds.