On Zero-Delay RDF for Vector-Valued Gauss-Markov Sources with Additional Noise
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We consider a zero-delay remote source coding problem where a hidden source modeled as time-invariant multidimensional Gauss-Markov process is partially observed through an encoder whereas the performance criterion is the mean squared-error (MSE) distortion between the hidden process and the reconstructed process. For this setup, we characterize a converse bound on the long term expected length of all instantaneous codes. This characterization is used to derive a closed form expression for stationary scalar-valued Gaussian processes which is well-defined only for a specific range of values of the distortion region. The obtained analytical solution is utilized to compute the rate-loss (RL) gap from the well-studied special case of “fully observable” scalar-valued Gauss-Markov processes obtained in [1, Eq. (1.43)] and to draw connections to existing results in the literature.
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