Real-time state estimation of linear processes over a shared awgn channel without feedback

We formulate the problem of estimating the state in real-time of multiple continuous-time linear dynamical systems over a shared Additive White Gaussian Noise (AWGN) channel without channel feedback and characterize the optimal encoders and decoder for minimum mean-squared error (MMSE) estimation. The first analyses are for a a single linear system being observed over an AWGN channel with a power constraint. One optimal encoder is a scaled innovation encoder and the decoder a scaling of the channel output. We then study the same problem for multiple linear systems communicating over a shared AWGN channel and characterize the optimal encoders and decoder. Finally the encoders and decoder are characterized in closed form for two identical linear sources with some correlation. We bound the optimal costs without the correlation assumption.