Definition (Distortion)

The distortion $D$ measures the expected or average distortion between a source and its reproduction $$D=E[d(X,\hat{X})]$$

Definition (Distortion measure)

The distortion measure is a measure, $d:\mathcal{X}\times\mathcal{X}\to[0,\infty)$, used to calculate the expected distortion.

Definition (Reproduction)

The reproduction of a source is a sequence $(\hat{X}_{i})_{i\in\mathbb{N}}$ from the reproduction alphabet $\hat{\mathcal{X}}$. i.e. it is the sequence of recovered symbols after the source has been broadcast over a channel.