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In this paper, we analyze the indirect source coding problem with sideinformation at both the encoder and decoder, as well as only at the decoder. Wefirst derive structural properties of the two rate distortion functions (RDFs)for general abstract spaces and identify conditions under which the RDFscoincide. For multivariate jointly Gaussian random variables with square-errorfidelity, we establish structural properties of the optimal test channels, showthat side information at both the encoder and decoder does not reducecompression, and provide water-filling solutions using parallel Gaussianchannel realizations. This paper uses a novel realization theory approach toestablish achievability of the converse coding theorem lower bounds of the twoRDFs.

Indirect Rate Distortion Functions with Side Information: Structural Properties and Multivariate Gaussian Sources