Lattice codes under imperfect channel state information

The performance of lattice coding and decoding for the ergodic fading point-to-point channel is studied in the presence of channel estimation errors at the receiver. We show that lattice codes achieve rates within a constant gap to that of Medard's scheme with Gaussian input. Interestingly, the gap does not depend on the channel estimation error variance nor the signal-to-noise ratio (SNR), for a wide range of fading distributions. The proposed scheme uses nested lattice codes in conjunction with decision regions that are universal in the sense that they only depend on the channel distribution and not the channel realizations. In addition, we introduce the generalized Degrees-of-Freedom (GDoF) as a figure of merit for channels with imperfect channel state information. It is shown that lattice codes achieve the same GDoF as that of Medard's Gaussian-input scheme.