Encoder-decoder design for perfect reconstruction: A robust control perspective

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 unknown. We are interested in designing transmitter-receiver pairs that perfectly reconstruct the discrete data with a given delay under all possible realizations of channel noise. A Decision Feedback Equalizer (DFE) structure is assumed for the receiver while a linear structure is imposed on the transmitter along with the requirement that the power of the transmission is limited. Under these circumstances, we build on our previous work to provide necessary and sufficient conditions for perfect reconstruction in terms of the l(1) norms of appropriate maps. An l(1) iteration procedure that results in parametric linear programs is developed to optimize the design parameters for the transmitter-receiver pair. This is done for both the (standard) case when no feedback from the receiver to the transmitter is available and for the case when feedback is available. When only a delayed binary decision is fed back to the transmitter, which is a special instance of the second case, we also provide an implementation for finite time error recovery in terms of an additional l(1) optimization.