Coding and control over discrete noisy forward and feedback channels

We consider the problem of stabilizability of remote LTI systems where both the forward (from the sensor to the controller) and the feedback (from the controller to the plant) channels are noisy, discrete, and memoryless. Information theory and the theory of Markov processes are used to obtain necessary and sufficient conditions (both structural and operational) for stabilizability, with the conditions being on error exponents, delay and source-channel codes. These results generalize some of the existing results in the literature which assume either the forward or the reverse channel to be noise-free. We observe that unlike continuous alphabet channels, discrete channels entail a substantial complexity in encoding the unbounded state and control spaces for control of noisy plants. We introduce a state-space encoding scheme utilizing the dynamic evolution. We also present variable-length coding through variable-sampling to transmit countably infinite symbols over a finite channel.