Proceedings ArticleDOI
Infinitely Many Information Inequalities
František Matúš
- pp 41-44
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TLDR
No finite set of linear combinations generates all such inequalities, so an infinite sequence of new linear information inequalities and a curve in a special geometric position to the halfspaces defined by the inequalities are proved.Abstract:
When finite, Shannon entropies of all sub vectors of a random vector are considered for the coordinates of an entropic point in Euclidean space. A linear combination of the coordinates gives rise to an unconstrained information inequality if it is nonnegative for all entropic points. With at least four variables no finite set of linear combinations generates all such inequalities. This is proved by constructing explicitly an infinite sequence of new linear information inequalities and a curve in a special geometric position to the halfspaces defined by the inequalities. The inequalities are constructed recurrently by adhesive pasting of restrictions of polymatroids and the curve ranges in the closure of a set of the entropic points.read more
Citations
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On characterization of entropy function via information inequalities
Zhen Zhang,Raymond W. Yeung +1 more
TL;DR: The main discovery of this paper is a new information-theoretic inequality involving four discrete random variables which gives a negative answer to this fundamental problem in information theory: /spl Gamma/~*/sub n/ is strictly smaller than /spl gamma// Sub n/ whenever n>3.
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