On source coding with side-information-dependent distortion measures

High-resolution bounds in lossy coding of a real memoryless source are cons idered when side information is present. Let X be a "smooth" source and let Y be the side information. First we treat the case when both the encoder a nd the decoder have access to Y and we establish an asymptotically tight th igh-resolution) formula for the conditional rate-distortion function R-X\Y( D) for a class of locally quadratic distortion measures which may be functi ons of th side information. We then consider the case when only the decoder has access to the side information (i.e., the "Wyner-Ziv problem"). For si de-information-dependent distortion measures, we give an explicit formula w hich tightly approximates the Wyner-Ziv rate-distortion function R-WZ(D) fo r small D under some assumptions on the joint distribution of X and Y. Thes e results demonstrate that for side-information-dependent distortion measur es the rate loss R-WZ(D) - R-X\Y(D) can be bounded away from zero in the li mit of small D. This contrasts the case of distortion measures which do not depend on the side information where the rate loss vanishes as D --> 0.