Equivalent models for multi-terminal channels

The recently introduced network equivalence results are used to create bit-pipe models that can replace multi-terminal channels within a discrete memoryless network. The goal is to create a set of simple “components” or “blocks” that can be substituted for the channel in such a way that the resulting network is capable of emulating the operation of the original one. We develop general upper and lower bounding models for the multiple access channel and for a class of broadcast channels. These bounds are sharp in the sense that there exists networks where the original channel can achieve the maximum sum rate permissible through the upper or lower bounding models. This approach provides a simple method for analyzing the capacity of large networks, which we illustrate with an example.