Beyond Shannon-Type Inequalities

Abstract

In Chapter 12, we introduced the regions Γ* _n and Γ _n in the entropy space H _n for n random variables. From Γ* _n , one in principle can determine whether any information inequality always holds. The region Γ _n , defined by the set of all basic inequalities (equivalently all elemental inequalities) involving n random variables, is an outer bound on Γ* _n . From Γ _n , one can determine whether any information inequality is implied by the basic inequalities. If so, it is called a Shannon-type inequality. Since the basic inequalities always hold, so do all Shannon-type inequalities. In the last chapter, we have shown how machineproving of all Shannon-type inequalities can be made possible by taking advantage of the linear structure of Γ _n .