On functionals satisfying a data-processing theorem

Abstract

It is shown that the rate-distortion bound <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(R(d) \leq C)</tex> remains true when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-\log x</tex> in the definition of mutual information is replaced by an arbitrary concave <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(\cup)</tex> nonincreasing function satisfying some technical conditions. Examples are given showing that for certain choices of the concave functions, the bounds obtained are better than the classical rate-distortion bounds.