Tradeoff between message and state information rates

We consider a communication problem where the sender has access to the channel state information and wishes to send both the message information and the state information across the channel. The novelty in characterizing the tradeoff between the message information rate and state estimation error arises primarily because of the instability of encoding and decoding the state information. The tradeoff region is typically difficult to obtain even for a simple channel. We characterize the optimal trade-off for the binary channel Yⁿ=Xⁿ⊕Sⁿ⊕Zⁿ, where Sⁿ is available at the transmitter. We also prove the optimality of the extreme points of the conjectured tradeoff region for the additive Gaussian channel Yⁿ=Xⁿ+Sⁿ+Zⁿ, with Sⁿ i.i.d.~N(0,Q) known at the encoder and unknown noise Zⁿ i.i.d.~N(0,N)