Rate sufficient conditions for closed-loop control over AWGN relay channels

The problem of remotely controlling an unstable noiseless linear time invariant system with Gaussian distributed initial state over two different noisy relay channels with average power constraints is considered. For information transmission over orthogonal half-duplex and non-orthogonal full-duplex relay channel, we propose a coding/decoding scheme based on Schalkwijk-Kailath scheme. Therefore, we derive conditions on rate which are sufficient for mean square stability of the linearly controlled LTI system over the given relay channels.