Achieving the ergodic capacity with lattice codes

The performance of lattice codes in the additive white Gaussian noise (AWGN) channel has attracted much attention lately, however, their performance under ergodic fading channels has been relatively unexplored. We show that lattice coding and decoding achieve the capacity of the ergodic point-to-point and multiple-access channels (MAC). Additionally, a low-complexity scheme is proposed for the ergodic MAC. At moderate and high signal-to-noise ratio (SNR), the sum rate achieved by the low-complexity scheme is within a constant gap to the ergodic MAC sum capacity, whereas at low SNR the gap to capacity diminishes quadratically with linear SNR decrease.