Average Entropy Functions

The closure of the set of entropy functions associated with n discrete variables, Gammarn, is a convex cone in (2n-1)- dimensional space, but its full characterization remains an open problem. In this paper, we map Gammarn to an n-dimensional region Phin by averaging the joint entropies with the same number of variables, and show that the simpler Phin can be characterized solely by the Shannon-type information inequalities