On the structure of the capacity region of the Gaussian multiple access channel

It is well-known that the capacity region of an M-user Gaussian multiple access channel is an M-dimensional polytope and the capacity region of a general discrete memoryless multiple-access channel contains a union of such polytopes. An expression for the number of vertices, edges, and more generally faces of any dimension D, of the capacity region of a Gaussian multiple access channel is derived in this paper.