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Large Deviation Theorems Revisited: Information-Spectrum Approach

Te-Sun HAN

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Summary :

In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.2704-2719
Publication Date
2008/10/01
Publicized
Online ISSN
1745-1337
DOI
10.1093/ietfec/e91-a.10.2704
Type of Manuscript
Special Section PAPER (Special Section on Information Theory and Its Applications)
Category
Information Theory

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