A Converse Bound Characterization on Zero-Delay Indirect RDF for Vector Gauss-Markov Sources
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We consider a zero-delay remote source coding problem where a hidden source modeled as a time-invariant vector-valued Gauss-Markov process is partially observed to an encoder whereas the performance criterion is the long-term mean squared-error (MSE) distortion between the hidden process and the reconstructed process. For this setup, we characterize a converse bound on the minimum long-term average length of all causal prefix-free codes. This characterization is then used to derive a novel closed form expression for stationary scalar-valued Gaussian processes. We justify the generality of our solution by revealing well-known special cases from it like the widely used analytical expression of sequential or nonanticipative RDF derived for "fully observable" stationary scalar-valued Gauss-Markov processes with MSE distortion constraint in [1], from which we also compute analytically the rate-loss (RL) gap from our solution.
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