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

Emirhan Gürpınar Andrei Romashchenko 1, 2
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01990325
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Submitted on : Wednesday, May 29, 2019 - 10:27:29 AM
Last modification on : Wednesday, May 13, 2020 - 3:02:09 PM

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

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