Entropy region and convolution

0465564 - ÚTIA 2017 RIV US eng J - Journal Article
Matúš, František - Csirmaz, L.
Entropy region and convolution.
IEEE Transactions on Information Theory. Roč. 62, č. 11 (2016), s. 6007-6018. ISSN 0018-9448. E-ISSN 1557-9654
R&D Projects: GA ČR GA13-20012S
Institutional support: RVO:67985556
Keywords : entropy region * information-theoretic inequality * polymatroid
Subject RIV: BD - Theory of Information
Impact factor: 2.679, year: 2016
http://library.utia.cas.cz/separaty/2016/MTR/matus-0465564.pdf

The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. Its shape is studied here by means of polymatroidal constructions, notably by convolution. The closure of the region is decomposed into the direct sum of tight and modular parts, reducing the study to the tight part. The relative interior of the reduction belongs to the entropy region. Behavior of the decomposition under selfadhesivity is clarified. Results are specialized and extended to the region constructed from four-tuples of random variables. This and computer experiments help to visualize approximations of a symmetrized part of the entropy region. The four-atom conjecture on the minimal Ingleton score is refuted.
Permanent Link: http://hdl.handle.net/11104/0265403