Optimal preprocessing strategies for perfect reconstruction of binary signals under power-constrained transmission

In this paper we further explore our deterministic worst-case framework for perfect reconstruction of discrete data transmissions through dispersive communication channels. Specifically, we are concerned with perfect reconstruction when the data can be processed in a way that does not increase the energy per-symbol (power). We obtain necessary and sufficient conditions for perfect reconstructability with power-limited preprocessing for two distinct cases: (i) the case of a single source-destination pair and (ii) the case of a single source with multiple destinations. In both cases, our conditions for perfect reconstructability are irrespective of the receiver structure. We also discuss via an example the trade-off that arises between the rate of transmission and the minimal power that is required for perfect reconstruction.