On channel coding with rate limited side information and its duality in source coding

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 encoder is informed with the encoder's side information (ESI, S₁) and the decoder is informed with the decoder's side information (DSI, S₂), and additionally, either the encoder or the decoder is also informed with a version of the other's side information with a rate limited to R̅_s. We derive six special cases of channel coding and source coding problems and we provide a single-letter characterization for the capacity or the rate distortion function for the different cases. We then present a duality between the channel capacity and the rate distortion for the cases we study.