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Source Coding in Networks with Covariance Distortion Constraints
We consider a source coding problem with a network scenario in mind, and
formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance
matrix distortions. We define a notion of minimum for two positive-definite
matrices based on which we derive an explicit formula for the rate-distortion
function (RDF). We then study the special cases and applications of this
result. We show that two well-studied source coding problems, i.e. remote
vector Gaussian Wyner-Ziv problems with mean-squared error and mutual
information constraints are in fact special cases of our results. Finally, we
apply our results to a joint source coding and denoising problem. We consider a
network with a centralized topology and a given weighted sum-rate constraint,
where the received signals at the center are to be fused to maximize the output
SNR while enforcing no linear distortion. We show that one can design the
distortion matrices at the nodes in order to maximize the output SNR at the
fusion center. We thereby bridge between denoising and source coding within
this setup
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