  The joint nonanticipative rate distortion function (NRDF) for a tuple of
random processes with individual fidelity criteria is considered. Structural
properties of optimal test channel distributions are derived. Further, for the
application example of the joint NRDF of a tuple of jointly multivariate
Gaussian Markov processes with individual square-error fidelity criteria, a
realization of the reproduction processes which induces the optimal test
channel distribution is derived, and the corresponding joint NRDF is
characterized. The analysis of the simplest example, of a tuple of scalar
correlated Markov processes, illustrates many of the challenging aspects of
such problems.
