Generalized cutoff rates and Renyi's information measures

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Abstract

Renyi's entropy and divergence of order α are given operational characterizations in terms of block coding and hypothesis testing, as so-called β-cutoff rates, with α = 1/1 + β for entropy and α = 1/1 - β for divergence. Out of several possible definitions of mutual information of order α (for channel W and input distribution P) we adopt Iα(P,W) = minQΣxP(x)Dα(W(·|x)∥Q). This admits interpretation as a β-cutoff rate, with α = 1/1 - β (at least for α ≥ 1/2 ), and so does maxpIα(P,W), the 'Renyi capacity.' Geometrically, the β-cutoff rate for a discrete memoryless source or channel is the τ-axis intercept of the tangent of slope β to the curve e(r), where c(τ) is the exponent of the probability of error resp, of correct decoding for the best codes of rate r, according as r is an achievable rate or not. The ordinary cutoff rate of a DMC is the β-cutoff rate with β = -1. The β-cutoff rate for hypothesis testing has a similar geometric representation, c(τ) being the exponent of convergence of the probability of type 2 error to 0 or 1, for the best tests of sample size n → ∞ with probability exp(-nτ) of type 1 error.

Original languageEnglish
Title of host publicationProceedings of the 1993 IEEE International Symposium on Information Theory
PublisherPubl by IEEE
Number of pages1
ISBN (Print)0780308786
Publication statusPublished - Jan 1 1993
EventProceedings of the 1993 IEEE International Symposium on Information Theory - San Antonio, TX, USA
Duration: Jan 17 1993Jan 22 1993

Publication series

NameProceedings of the 1993 IEEE International Symposium on Information Theory

Other

OtherProceedings of the 1993 IEEE International Symposium on Information Theory
CitySan Antonio, TX, USA
Period1/17/931/22/93

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ASJC Scopus subject areas

  • Engineering(all)

Cite this

Csiszar, I. (1993). Generalized cutoff rates and Renyi's information measures. In Proceedings of the 1993 IEEE International Symposium on Information Theory (Proceedings of the 1993 IEEE International Symposium on Information Theory). Publ by IEEE.