On the role of feedback in the design of perfectly reconstructing equalizers

In this paper we consider the transmission of discrete data via a communication channel that is subject to (additive) noise with a known upper bound on its magnitude but otherwise completely unrestricted behavior. We are interested in the characterization of general conditions that allow perfect reconstruction of the discrete data (perhaps with some delay) under all possible realizations of channel noise and under a limit on transmission power. In particular, we investigate how linear preprocessing of the data and/or linear feedback from the receiver can be employed to aid perfect reconstruction, and we provide necessary conditions for improvements in perfect reconstruction in terms of lscr¹ norms of appropriate maps. Finally, we show that perfect reconstruction can be improved with feedback only if the feedback processing contains unstable poles.