Approaching the ergodic capacity with lattice coding

It is known that lattice coding can achieve the capacity of the additive white Gaussian noise (AWGN) channel. This paper addresses the performance of lattice codes in the ergodic fading channel. Using nested lattice codes and ambiguity decoding, we show that the rates achieved by lattice coding and decoding are within a constant gap of the capacity of the ergodic channel at moderate and high signal-to-noise-ratio (SNR), and within a gap that decreases quadratically with the SNR for the low SNR regime.