Message transmission and state estimation over Gaussian broadcast channels

Motivated by [1], we consider the problem of simultaneous message transmission and state estimation over Gaussian broadcast channels. In particular, two independent messages are transmitted over a state dependent Gaussian broadcast channel with noncausal side information at the transmitter. The receivers, in addition to decode their own messages, also try to estimate the state information. Using squared-error distortion, we provide in this paper an inner bound and an outer bound for the optimal rate distortion tradeoff.