Approaching the Ergodic Capacity of Wireless Networks with Lattice Code

Despite significant progress in the area of lattice coding and decoding, their operation under ergodic fading has been mostly unexplored. In this dissertation, lattice coding and decoding are studied for several ergodic fading scenarios, and their performance is analyzed. The channels under study are the multiple-input-multiple-output (MIMO) point-to-point channel, the multiple-access channel (MAC), the dirty paper channel, the broadcast channel and the interference channel. The channels are stationary and ergodic with time-varying gain. Different scenarios of channel state information are studied, including the availability of channel state information at the receiver (CSIR), and the case of availability of channel state information at the transmitter (CSIT) as well. For the point-to-point channel, the case of noisy channel state information at the receiver is also considered. Motivated by practical considerations, the proposed decoding rule for the different models under study is fixed for a given channel distribution and does not depend on the instantaneous realizations of the channel. When the channel state information is available at all communication nodes, it is shown that lattice codes achieve the capacity of the MIMO point-to-point channel as well as the K-user broadcast channel. When the channel state information is available at the receiver, it is shown that the gap to capacity is a constant that diminishes with the number of receive antennas, even at finite signal-to-noise ratio (SNR) for the MIMO Rayleigh fading channels under study. Single-input-single-output (SISO) channels are also considered, where the decoding process is simpler and the gap to capacity is shown to be bounded by a constant for a wide range of fading distributions. The same behavior follows for the MAC results. Additionally, an alternative decoding approach is presented for block-fading SISO point-to-point channels that are drawn from a discrete distribution, where channel-matching decision regions are proposed. The gap to capacity is shown to be a constant that diminishes under special cases. The fading MIMO dirty paper channel with CSIR is also studied, where a lattice coding/decoding scheme achieves a constant gap to capacity. A tighter inner bound for the channel is also developed using Gaussian codebooks in conjunction with random binning. Results are extended to MIMO broadcast channels with CSIR, where the results are compared to newly developed outer bounds for the broadcast channel. Finally, the two-user fading interference channel is studied under the ergodic strong regime. The capacity region of this channel is developed using Gaussian coding, and a lattice coding/decoding scheme is proposed and its achievable rate region is computed, whose gap to capacity is shown to be fairly small.