On a Relationship between the Correct Probability of Estimation from Correlated Data and Mutual Information

Yasutada OOHAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2205-2209
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2205
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Shannon theory
mutual information,  correct probabilty of decoding,  one helper source coding problem,  

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Let X, Y be two correlated discrete random variables. We consider an estimation of X from encoded data φ(Y) of Y by some encoder function φ(Y). We derive an inequality describing a relation of the correct probability of estimation and the mutual information between X and φ(Y). This inequality may be useful for the secure analysis of crypto system when we use the success probability of estimating secret data as a security criterion. It also provides an intuitive meaning of the secrecy exponent in the strong secrecy criterion.