Polymatroidal structure in the multiple access channel with general message sets

The conditions which govern reliable communication over networks are often given as a union of polyhedra. As increasingly larger networks are considered, these conditions become unwieldy and intractable, unless useful structure can be found in them. An example of a polyhedron with a useful underlying structure is a polymatroid, which despite its exponential number of defining inequalities, has a simple and explicit formula for its vertices. For the multiple access channel with general message sets, we show that each capacity characterization in a large class of capacity characterizations involves polymatroids.