Source-channel communication with feedback

Feedback may greatly simplify the coding techniques needed to achieve the (information-theoretically) optimum performance. This is true both for the capacity problem and for the joint source-channel coding problem. We are interested in the latter. Gaussian examples involving feedback have appeared in the literature (Cruise, T.J., 1967; Kailath, T., 1967; Schalkwijk, J.P.M. and Bluestein, L.I., 1967). We present a general matching condition for source-channel communication with feedback, extending our previous results for the case without feedback (Gastpar, M. et al., Proc. IEEE Int. Symp. Inf. Theory, p.236, 2000; IEEE Trans. Inf. Theory, 2003). This condition permits, for example, the characterizing of instances of source/channel pairs for which very simple yet optimal feedback coding strategies exist, and leads to an understanding of the potential offered by feedback, and how to exploit it.