A general approach to random coding for multi-terminal networks

We introduce a general framework to derive achievable rate regions based on random coding for any memoryless, single-hop, multi-terminal network. We show that this general inner bound may be obtained from a graph representation that captures the statistical relationship among codewords and allows one to readily obtain the rate bounds under which the error probability vanishes as the block-length goes to infinity. The proposed graph representation naturally leads to an "automatic rate region derivator" which produces achievable rate regions combining classic random coding techniques such as coded timesharing, rate-splitting, superposition coding and binning for the general memoryless network under consideration.