Coding for the Feedback Gel´fand–Pinsker Channel and the Feedforward Wyner–Ziv Source

We consider both channel coding and source coding, with perfect past feedback/feedforward, in the presence of side information. It is first observed that feedback does not increase the capacity of the Gel´fand-Pinsker channel, nor does feedforward improve the achievable rate-distortion performance in the Wyner-Ziv problem. We then focus on the Gaussian case showing that, as in the absence of side information, feedback/feedforward allows to efficiently attain the respective performance limits. In particular, we derive schemes via variations on that of Schalkwijk and Kailath. These variants, which are as simple as their origin and require no binning, are shown to achieve, respectively, the capacity of Costa´s channel, and the Wyner-Ziv rate distortion function. Finally, we consider the finite-alphabet setting and derive schemes for both the channel and the source coding problems that attain the fundamental limits, using variations on schemes of Ahlswede and Ooi and Wornell, and of Martinian and Wornell, respectively