Rate distortion theory with generalized information measures via convex programming duality

A new generalized average mutual information measure (GAMIM) is introduced in terms of Csiszar
\phi
-divergence, and the associated rate distortion function
R_{\phi}
is studied. The main objective is to derive in a unified way a dual representation of
R_{\phi}
, then to use it to generalize classical results (corresponding to
\phi(t) = t \log t
) in rate distortion theory and extend results associated with other concepts of GAMIM. Our development uses the methodology of convex programming duality extensively.