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Networked Source Coding with Covariance Distortion Constraints

We consider a source coding problem under covariance matrix distortions with side information available at the decoder. With a networked scenario in mind, the side information models the availability of other observations at the receiver. We formulate the problem as a remote vector Gaussian Wyner-Ziv problem, and derive an explicit and general formula for the corresponding rate-distortion function (RDF). We demonstrate the flexibility and generality of the covariance matrix distortions using three application examples. In the first two, we show that two other well-studied source coding problems are in fact special cases of our results for particular choices of the distortion matrices. As the last and most elaborated example of applications, we consider a network with a centralized topology with a given weighted sum-rate constraint. The received data at the center are to be fused to maximize the output SNR while enforcing no linear distortion to the processed output. We will show that one could design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center, and thereby bridge between enhancement and source coding within this setup.