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

Abstract

Let (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1, i</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,i</sub> ) ~ i.i.d p(s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ), 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, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) and the decoder is informed with the decoder's side information (DSI, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ), 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . 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.