Vector Gaussian Rate-Distortion with Variable Side Information

Abstract

We consider rate-distortion with two decoders, each with distinct side information. This problem is well understood when the side information at the decoders satisfies a certain degradedness condition. We consider cases in which this degradedness condition is violated but the source and the side information consist of jointly Gaussian vectors. We provide a hierarchy of four lower bounds on the optimal rate. These bounds are then used to determine the optimal rate for several classes of instances.

Presented in parts at the IEEE Int. Symposium on Information Theory (ISIT), Hawaii, July 2014, the Information Theory and Applications Workshop, Jan./Feb. 2016, and the Conference on Information Sciences and Systems (CISS), Princeton, March 2016. Submitted to IEEE Transactions on Information Theory