A construction of entropic vectors

The problem of determining the region of entropic vectors is a central one in information theory. Recently, there has been a great deal of interest in the development of non-Shannon information inequalities, which provide outer bounds to the aforementioned region; however, there has been less recent work on developing inner bounds. This paper develops an inner bound that applies to any number of random variables and which is tight for 2 and 3 random variables (the only cases where the entropy region is known). The construction is based on probability distributions generated by a lattice. The region is shown to be a polytope generated by a set of linear inequalities. It can therefore be used to compute an inner bound on the information-theoretic capacity region for a wide class of network problems using linear programming.