Beyond Shannon-Type Inequalities
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 .
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