Upper concave envelopes and auxiliary random variables

We propose a new characterization of inner and outer bounds of some network information theoretic regions in terms of upper concave envelopes of certain functions of mutual information. While this characterization is related to the characterization using auxiliary random variables, it is shown that the new characterization can make computations of boundary points much simpler. Further this representation also leads to some new kinds of factorization inequalities concerning information theoretic quantities. It also provides some new pathways into proving optimality of certain achievable rate regions.