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Entropy 2011, 13(2), 379-401; doi:10.3390/e13020379

Recent Progresses in Characterising Information Inequalities

Institute for Telecommunications Research, University of South Australia, Australia
Received: 1 December 2010 / Revised: 19 January 2011 / Accepted: 28 January 2011 / Published: 31 January 2011
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Abstract

In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery of this non-Shannon inequality is a breakthrough in the area and has led to the subsequent discovery of many more non-Shannon inequalities. We will also review the close relations between information inequalities and other research areas such as Kolmogorov complexity, determinantal inequalities, and group-theoretic inequalities. These relations have led to non-traditional techniques in proving information inequalities and at the same time made impacts back onthose related areas by the introduction of information-theoretic tools.
Keywords: determinantal inequalities; Greene’s Theorem; Kolmogorov complexity; quasi-uniformity; Shannon entropies; subspace rank inequalities

determinantal inequalities; Greene’s Theorem; Kolmogorov complexity; quasi-uniformity; Shannon entropies; subspace rank inequalities

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Chan, T. Recent Progresses in Characterising Information Inequalities. Entropy 2011, 13, 379-401.

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