A perfect reconstruction paradigm for digital communication

In this paper we present a deterministic worst-case framework for reconstruction of discrete data transmissions through dispersive communication channels. This framework can be explored based on robust control ideas and formulations and serves as a complement to existing approaches that reconstruct data by optimizing probabilistic criteria. The particular problems touched upon are: (i) necessary and sufficient conditions for causal and non-causal perfect reconstruction under deterministic magnitude bounded noise for single-input single-output (SISO) and multi-input multi-output (MIMO) channels, (ii) perfect reconstruction based on decision feedback equalizer (DFE) structures, and (iii) necessary and sufficient conditions for perfect reconstruction with DFEs in the presence of channel fading. The ℓ¹ control theory emerges as the natural key player for analysis and synthesis of perfectly reconstructing receivers in this framework.