An Achievable Region for a General Multi-terminal Network and the corresponding Chain Graph Representation

Random coding, along with various standard techniques such as coded time-sharing, rate-splitting, superposition coding,and binning, are traditionally used in obtaining achievable rate regions for multi-terminal networks. The error analysis of suchan achievable scheme relies heavily on the properties of strongly joint typical sequences and on bounds of the cardinality oftypical sets. In this work, we obtain an achievable rate region for a general (i.e. an arbitrary set of messages shared amongstencoding nodes, which transmit to arbitrary decoding nodes) memoryless, single-hop, multi-terminal network without feedback orcooperation by introducing a general framework and notation, and carefully generalizing the derivation of the error analysis. Weshow that this general inner bound may be obtained from a chain graph representation of the encoding operations. This graphrepresentation captures the statistical relationship among codewords and allows one to readily obtain the rate bounds that define theachievable rate region. The proposed graph representation naturally leads to the derivation of all the achievable schemes that canbe generated by combining classic random coding techniques for any memoryless network used without feedback or cooperation.We also re-derive a few achievable regions for classic multi-terminal networks, such as the multi-access channel, the broadcastchannel, and the interference channel, to show how this new representation allows one to quickly consider the possible choicesof encoding/decoding strategies for any given network and the distribution of messages among the encoders and decoders.