About the Mutual (Conditional) Information

Renato Renner and Ueli Maurer

IEEE International Symposium on Information Theory — ISIT 2002, IEEE, pp. 364, Jun 2002, This is the Proceedings version of [RenMau02a].

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.

BibTeX Citation

@inproceedings{RenMau02b,
    author       = {Renato Renner and Ueli Maurer},
    title        = {About the Mutual (Conditional) Information},
    booktitle    = {IEEE International Symposium on Information Theory --- ISIT 2002},
    pages        = {364},
    year         = {2002},
    month        = {6},
    note         = {This is the Proceedings version of \cite{RenMau02a}},
    publisher    = {IEEE},
}