Approaching the Ergodic Capacity of Wireless Networks with Lattice Codes




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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. Specifically, 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 are studied under stationary and ergodic fading, with channel state information available only at the receiver (CSIR), or channel state also available at the transmitter (CSIT). 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 rules are only a function of channel statistics and do 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 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) under Rayleigh fading. 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 conclusion follows for the MAC. 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 mild conditions. The fading MIMO dirty paper channel with CSIR is also studied, where a lattice coding/decoding scheme achieves a constant gap to capacity. An inner bound for the dirty paper channel is also developed using Gaussian codebooks in conjunction with random binning. Results are extended to MIMO broadcast channels with CSIR, and 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 calculated using Gaussian codebooks. In addition, a lattice coding/decoding scheme is proposed, and its achievable rate region is computed, whose gap to capacity is shown to be small.



Ergodic theory, Lattice theory, MIMO systems, Decoders (Electronics)


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