The Capacity Region for Multi-source Multi-sink Network Coding

The capacity problem for general acyclic multi- source multi-sink networks with arbitrary transmission requirements has been studied by L. Song, et al (2003). Specifically, inner and outer bounds of the capacity region were derived respectively in terms of Gamman* and Gamma macrn*, the fundamental regions of the entropy function. In this paper, we show that by carefully bounding the constrained regions in the entropy space, we obtain the exact characterization of the capacity region, thus closing the existing gap between the above inner and outer bounds.