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Publications: Abstract

About the Mutual (Conditional) Information

Renato Renner and Ueli Maurer

We give a necessary, sufficient, and easily verifiable criterion for the conditional probability distribution $P_{Z|XY}$ (where $X$, $Y$ and $Z$ are arbitrary random variables), such that $I(X;Y) \geq I(X;Y|Z)$ holds for any distribution $P_{XY}$. Furthermore, the result is generalized to the case where $Z$ is specified by a conditional probability distribution depending on more than two random variables.