Gaussian Broadcast Channel with State Estimation

A state amplification problem, where the common
additive state to a Gaussian broadcast channel (BC) is to be
estimated at both receivers, is considered. The state process,
known non-causally at the encoder, is assumed to be independent
and identically distributed (i.i.d.) Gaussian. Both receivers must
estimate the state process to within acceptable squared error
distortion limits. In addition to the state estimation, our setting
also requires message transmission to the stronger receiver at a
given rate. We are interested in the optimal trade-offs between the
distortions incurred at the receivers when a message at a given
rate is to be delivered from the encoder to the strong receiver. A
complete characterization of the rate-distortion trade-off region
is presented. Our result differs from a recent result where an
additional common reconstruction constraint was imposed on
the state estimates in the same setting, and it was observed that
allowing the weak user to decode part of the private message to
the stronger user helps the distortion trade-offs.