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Conference Papers Year : 2019

How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma

Abstract

We discuss linear programming techniques that help to deduce corollaries of non classic inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown) non-classic universal inequalities for Shannon's entropy, though we do not derive these inequalities explicitly. To reduce the computational complexity of these problems, we extensively use symmetry considerations. We present two examples of usage of these techniques: we provide a reduced size formal inference of the best known bound for the Ingleton score (originally proven by Dougherty et al. with explicitly derived non Shannon type inequalities), and improve the lower bound for the optimal information ratio of the secret sharing scheme for an access structure based on the Vamos matroid.
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Dates and versions

lirmm-01990325 , version 1 (29-05-2019)

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Emirhan Gürpınar, Andrei Romashchenko. How to Use Undiscovered Information Inequalities: Direct Applications of the Copy Lemma. ISIT 2019 - IEEE 1st International Symposium on Information Theory, Jul 2019, Paris, France. pp.1377-1381, ⟨10.1109/ISIT.2019.8849309⟩. ⟨lirmm-01990325⟩
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