Gauss–Markov Source Tracking with Side Information: Lower Bounds

We consider the problem of causal source coding and causal decoding of a Gauss-Markov source, where the decoder has causal access to a side-information signal. We define the information causal rate-distortion function with causal decoder side information and prove that it bounds from below its operational counterpart. We further explain how to adapt the result to the setting of control over communication channels.