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Entropy 2008, 10(4), 765-775; doi:10.3390/e10040765
Article

Non-linear Information Inequalities

*  and
Institute for Telecommunications Research, University of South Australia, Australia
* Author to whom correspondence should be addressed.
Received: 24 May 2008 / Accepted: 9 December 2008 / Published: 22 December 2008
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Abstract

We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.
Keywords: Entropy; entropy function; nonlinear information inequality; nonshannon type information inequality Entropy; entropy function; nonlinear information inequality; nonshannon type information inequality
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Chan, T.; Grant, A. Non-linear Information Inequalities. Entropy 2008, 10, 765-775.

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