On functionals satisfying a data-processing theorem

It is shown that the rate-distortion bound
(R(d) \leq C)
remains true when
-\log x
in the definition of mutual information is replaced by an arbitrary concave
(\cup)
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.