Entropy Region and Convolution

Matus, Frantisek and Csirmaz, László (2016) Entropy Region and Convolution. IEEE TRANSACTIONS ON INFORMATION THEORY, 62 (11). pp. 6007-6018. ISSN 0018-9448


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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 self-adhesivity 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. © 2016 IEEE.

Item Type: Article
Uncontrolled Keywords: ENTROPY; Shannon; Polymatroids; Random variables; Matrix algebra; INFORMATION THEORY; Zhang-Yeung inequality; selfadhesivity; polymatroid; non-Shannon inequality; Matroid; Ingleton score; Ingleton inequality; information-theoretic inequality; four-atom conjecture; Entropy region; Entropy function; Convolution
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: MTMT SWORD
Date Deposited: 14 Nov 2017 10:30
Last Modified: 14 Nov 2017 10:30

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