Multi-way communication is a means to significantly improve the
spectral efficiency of wireless networks. This monograph provides
an overview of the developments in this research area since it was
initiated by Claude Shannon. The basic two-way communication
channel is considered first, followed by the two-way relay channel
obtained by the deployment of an additional cooperative relay node
to improve the overall communication performance. This basic setup
is then extended to multi-user systems. For all these setups,
fundamental limits on the achievable rates are reviewed, making use
of a linear high-SNR deterministic channel model to provide
valuable insights that are helpful when discussing of the coding
schemes for Gaussian channel models in detail. Several tools and
communication strategies are used in the process, including
computation, signal-space alignment, and nested lattice codes.
Finally, extensions of multi-way communication channels to multiple
antenna settings are discussed. This monograph provides a starting
point for any researcher or student in understanding this important
topic central to wireless communication systems.
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