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On a Construction of Entropic Vectors Using Lattice-Generated Distributions

Hassibi, Babak and Shadbakht, Sormeh (2007) On a Construction of Entropic Vectors Using Lattice-Generated Distributions. In: IEEE International Symposium on Information Theory, 2007. ISIT 2007. IEEE , Piscataway, NJ, pp. 501-505. ISBN 978-1-4244-1397-3.

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The problem of determining the region of entropic vectors is a central one in information theory. Recently, there has been a great deal of interest in the development of non-Shannon information inequalities, which provide outer bounds to the aforementioned region; however, there has been less recent work on developing inner bounds. This paper develops an inner bound that applies to any number of random variables and which is tight for 2 and 3 random variables (the only cases where the entropy region is known). The construction is based on probability distributions generated by a lattice. The region is shown to be a polytope generated by a set of linear inequalities. Study of the region for 4 and more random variables is currently under investigation.

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ID Code:54402
Deposited By: Shirley Slattery
Deposited On:09 Feb 2015 18:07
Last Modified:10 Nov 2021 20:33

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