State estimation codes for perfect secrecy

We study the problem of remote state estimation, in the presence of a passive eavesdropper. An authorized user estimates the state of an unstable linear plant, based on the packets received from a sensor, while the packets may also be intercepted by the eavesdropper. Our goal is to design a coding scheme at the sensor, which encodes the state information, in order to impair the eavesdropper's estimation performance, while enabling the user to successfully decode the sent messages. We introduce a novel class of codes, suitable for real-time dynamical systems, termed State-Secrecy Codes. By using acknowledgment signals from the user, they apply linear time-varying transformations to the current and previously received states. We prove that under minimal conditions, State-Secrecy Codes achieve perfect secrecy, namely the eavesdropper's minimum mean square error grows unbounded almost surely, while the user's estimation performance is optimal. These conditions require that at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. The theoretical results are illustrated in simulations.