On non-causal side information at the encoder

The problem of state communication over a discrete memoryless channel with discrete memoryless state is studied when the state information is available non-causally at the encoder. When the same channel is used to send additional independent information at the expense of a higher channel state estimation error, the optimal tradeoff between the rate of the independent information and the state estimation error is characterized via the capacity-distortion function. Information-theoretic lower and upper bounds (based respectively on ideas from hybrid-coding and rate-distortion theory) are derived on the capacity-distortion function. Some examples are provided, for which the capacity-distortion functions are characterized by showing that the two bounds match. These coding theorems are then extended to the case of source coding with side information vending machine at the encoder (introduced in [1]) to provide an improved lower bound on the rate-distortion function.