On Designing Probabilistic Supports to Map the Entropy Region

The boundary of the entropy region has been shown to determine fundamental inequalities and limits in key problems in network coding, streaming, distributed storage, and coded caching. The unknown part of this boundary requires nonlinear constructions, which can, in turn, be parameterized by the support of their underlying probability distributions. Recognizing that the terms in entropy are submodular enables the design of such supports to maximally push out towards this boundary.