Definition (Rate distortion function)

The rate distortion function of a source $X$ with respect to its distortion measure $d$, is defined for any Distortion $D\ge{0}$ by $$R(D)=\min_{p(\hat{x}|x):E[d(X,\hat{X})]\le D}I(X;\hat{X})$$

Definition (Distortion rate function)

The distortion rate function, $D(R)$, is the inverse of the rate distortion function. It represents the lowest achievable distortion with codes of rates less than $R$.