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The joint nonanticipative rate distortion function (NRDF) for a tuple ofrandom processes with individual fidelity criteria is considered. Structuralproperties of optimal test channel distributions are derived. Further, for theapplication example of the joint NRDF of a tuple of jointly multivariateGaussian Markov processes with individual square-error fidelity criteria, arealization of the reproduction processes which induces the optimal testchannel distribution is derived, and the corresponding joint NRDF ischaracterized. The analysis of the simplest example, of a tuple of scalarcorrelated Markov processes, illustrates many of the challenging aspects ofsuch problems.

Joint Nonanticipative Rate Distortion Function for a Tuple of Random Processes with Individual Fidelity Criteria