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Conditional Information Inequalities for Entropic and Almost Entropic Points

Abstract : We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be extended to any unconditional linear inequalities. Some of these conditional inequalities hold for almost entropic points, while others do not. We also discuss some counterparts of conditional information inequalities for Kolmogorov complexity.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00848455
Contributor : Andrei Romashchenko <>
Submitted on : Friday, July 26, 2013 - 10:40:42 AM
Last modification on : Wednesday, May 13, 2020 - 3:02:09 PM

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Tarik Kaced, Andrei Romashchenko. Conditional Information Inequalities for Entropic and Almost Entropic Points. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2013, 59 (11), pp.7149-7167. ⟨10.1109/TIT.2013.2274614⟩. ⟨lirmm-00848455⟩

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