State-Dependent Fading Gaussian Channel with Common Reconstruction Constraints

The task of jointly communicating a message and reconstructing a common estimate of the channel state is examined for a fading Gaussian model with additive state interference. The state is an independent and identically distributed Gaussian sequence known noncausally at the transmitter, and the instantaneous fading coefficient is perfectly known at both the transmitter and the receiver. The receiver is required to decode the transmitted message and, in addition, reconstruct the state under a common reconstruction constraint ensuring that its estimate coincides with that at the transmitter. A complete characterization of the optimal rate distortion tradeoff region for this setting is the main result of our work. The analytical results are also validated through numerical examples illustrating the rate distortion and power distortion tradeoffs.