Channel coding and source coding with increased partial side information

Let (S_1,i, S_2,i) ~ i.i.d p(s₁, s₂), i = 1, 2, ... be a memoryless, correlated partial side information sequence. In this work, we study channel coding and source coding problems where the partial side information (S₁, S₂) is available at the encoder and the decoder, respectively, and, additionally, either the encoder's or the decoder's side information is increased by a limited-rate description of the other's partial side information. We derive six special cases of channel coding and source coding problems and we characterize the capacity and the rate-distortion functions for the different cases. We present a duality between the channel capacity and the rate-distortion cases we study. In order to find numerical solutions for our channel capacity and rate-distortion problems, we use the Blahut-Arimoto algorithm and convex optimization tools. Finally, we provide several examples corresponding to the channel capacity and the rate-distortion cases we presented.