An Implicit Characterization of the Achievable Rate Region for Acyclic Multisource Multisink Network Coding

The achievable information rate region problem of multisource multisink network coding for general acyclic networks with arbitrary transmission requirements has previously been studied, where inner and outer bounds on the region were derived in terms of $\Gamma^{\ast}$ , the fundamental region of entropy functions. In this paper, we derive the exact characterization of the achievable rate region in terms of entropic functions, thus closing the gap between the existing inner and outer bounds.