A Coding Theorem for f-Separable Distortion Measures

In this work we relax the usual separability assumption made in rate-distortion literature and propose [Formula: see text]-separable distortion measures, which are well suited to model non-linear penalties. The main insight behind [Formula: see text]-separable distortion measures is to define an n-letter distortion measure to be an [Formula: see text]-mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with [Formula: see text]-separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions. Finally, we discuss connections between [Formula: see text]-separable distortion measures, and the subadditive distortion measure previously proposed in literature.