On the mutual information between random variables in networks

This paper presents a lower bound on the mutual information between any two sets of source/edge random variables in a general multi-source multi-sink network. This bound is useful to derive a new class of better information-theoretic upper bounds on the network coding capacity given existing edge-cut based bounds. A refined functional dependence bound is characterized from the functional dependence bound using the lower bound. It is demonstrated that the refined versions of the existing edge-cut based outer bounds obtained using the mutual information lower bound are stronger.