Feedback Communication with Reduced Delay over Noisy Time-Dispersive Channels

Using a framework that lies at the intersection of communications, estimation and control, this work considers feedback communication over noisy Gaussian feedforward as well as unconstrained feedback Time Dispersive Channels (TDCs), and presents a linear scheme that reduces transmission delay for a fixed encoder dimension. The approach is based on Liu and Elia's feedback scheme, that is generalized in this paper to accommodate a noisy TDC in the feedback link, showing the usefulness of the technique despite the noisy feedback. This technique also mitigates the inherent numerical instability problem in Liu and Elia's original system, and does not require the solution of a non-convex optimization problem to find the optimal encoder/decoder for a given pair of feedforward and feedback channels. These advantages are achieved at the expense of an increase in transmission power, that becomes small when the SNR increases. Computer simulation results show that the new scheme reduces significantly the transmission delay, while still providing rates at high SNR that are close to those achieved by an optimal linear encoder. These features make the new coding scheme attractive for practical applications.