Inflated Lattice Precoding, Bias Compensation, and the Uplink/Downlink Duality: The Connection

We review the uplink/downlink duality between decision-feedback equalization (DFE) and (nonlinear) precoding at the transmitter side. Thereby the effect of bias compensation in DFE is addressed, and its connection to the concept of "inflated lattice preceding" (ILP)-a tool which has been proven to be the key to achieve the capacity of channels with interference known at the transmitter-is elucidated. Concentrating on signal-to-interference plus noise ratios and hence error rates, pairs of schemes dual to each other are identified. It is shown that bias compensation in DFE and the scaling in ILP are dual operations and cancel each other