Unified duality between channel capacity and rate distortion with state information

We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We also present a unified theory for different cases of channel capacity with state information, which extends existing results to arbitrary pairs of i.i.d. state information (S₁, S₂) available at the sender and at the receiver, respectively. The general formula C=max(p(u, |s₁))[I(U; S₂, Y)-I(U; S₁)] assumes the same form as the Wyner-Ziv rate distortion function with state information. The Wyner-Ziv formula also unifies four special cases of the rate distortion problem with the state information