Logarithmic Sobolev Inequalities for Information Measures

For alpha ges 1 , the new Vajda-type information measure J alpha (X ) is a quantity generalizing Fisher's information (FI), to which it is reduced for alpha = 2 . In this paper, a corresponding generalized entropy power N alpha (X ) is introduced, and the inequality N alpha (X ) J alpha ( X ) g...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 55; no. 6; pp. 2554 - 2561
Main Authors:	Kitsos, C.P., Tavoularis, N.K.
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01-06-2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Applied sciences Calibration Convolution Cramer-Rao bounds Density measurement Design for experiments Educational technology Entropy Exact sciences and technology Fisher's measure of information Gaussian distribution Inequalities Information processing Information theory Information, signal and communications theory logarithmic Sobolev inequalities (LSIs) Mathematics Shannon and RÉnyi entropy Statistical analysis Telecommunications and information theory Vajda measure of information Vector space Information measure Convolution Fisher's measure of information Shannon and Rényi entropy Logarithmic function Vajda measure of information logarithmic Sobolev inequalities (LSIs) Entropy Renyi theory Shannon theory Fisher information
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Summary:	For alpha ges 1 , the new Vajda-type information measure J alpha (X ) is a quantity generalizing Fisher's information (FI), to which it is reduced for alpha = 2 . In this paper, a corresponding generalized entropy power N alpha (X ) is introduced, and the inequality N alpha (X ) J alpha ( X ) ges n is proved, which is reduced to the well-known inequality of Stam for alpha = 2 . The cases of equality are also determined. Furthermore, the Blachman-Stam inequality for the FI of convolutions is generalized for the Vajda information J alpha (X ) and both families of results in the context of measure of information are discussed. That is, logarithmic Sobolev inequalities (LSIs) are written in terms of new more general entropy-type information measure, and therefore, new information inequalities are arisen. This generalization for special cases yields to the well known information measures and relative bounds.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2009.2018179