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Book Inequalities.
- Source :
-
IEEE Transactions on Information Theory . Nov2014, Vol. 60 Issue 11, p6811-6818. 8p. - Publication Year :
- 2014
-
Abstract
- Information theoretical inequalities have strong ties with polymatroids and their representability. A polymatroid is entropic if its rank function is given by the Shannon entropy of the subsets of some discrete random variables. The book is a special iterated adhesive extension of a polymatroid with the property that entropic polymatroids have \(n\) -page book extensions over an arbitrary spine. We prove that every polymatroid has an \(n\) -page book extension over a single element and over an all-but-one-element spine. Consequently, for polymatroids on four elements, only book extensions over a two-element spine should be considered. Matúš proved that the Zhang–Yeung inequalities characterize polymatroids on four elements which have such a two-page book extension. The \(n\) -page book inequalities, defined in this paper, are conjectured to characterize polymatroids on four elements which have \(n\) -page book extensions over a two-element spine. We prove that the condition is necessary; consequently, every book inequality is an information inequality on four random variables. Using computer-aided multiobjective optimization, the sufficiency of the condition is verified up to nine-page book extensions. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 60
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 99041676
- Full Text :
- https://doi.org/10.1109/TIT.2014.2352273