Sufficient conditions for stabilizability over Gaussian relay and cascade channels

We present sufficient conditions for stabilizability of an unstable linear time invariant scalar system across an additive white Gaussian noise channel, with a relay assisting the observer. We consider two topologies: (i) a Gaussian relay channel, and (ii) a cascade of two Gaussian point to point channels. We assume that the control action is available at the relay, and that there are average power constraints on both the transmitter and the relay nodes. We propose coding schemes based on distributed stochastic approximation algorithms, and present sufficient conditions for the stabilizability of the plant through such schemes. The analysis suggests it may be useful to provide a relay node, even if the total transmission power remains the same.