The broad objective of this thesis is to explore the fundamental limits of communication over outage-limited wireless fading channels (including point-to-point and some multi-user scenarios), and design coding schemes that perform close to these limits.;In the first part of this thesis, we deal with the point-to-point multiple-input multiple-output (MIMO) channel. We present codes derived from lattices and cyclic division algebras that achieve the diversity-multiplexing tradeoff (DMT) of MIMO channels, and further have excellent performances in terms of codeword error probability at practical signal-to-noise ratios. Subsequently, we analyse the performance limits in terms of the DMT of such optimal codes over correlated Rayleigh and Rician MIMO channels, which model wireless channels observed in practice. We then shift our attention to receiver design, and characterize the performance of low-complexity linear MIMO receivers that are currently being considered as promising candidates for practical implementations.;Having treated the three major components of a point-to-point MIMO communication system viz., the encoder, channel and decoder, we shift our attention to multi-user problems. We first consider the single relay fading channel, and derive the DMT for finite block-length transmission under a dynamic decode and forward protocol. We also present practical codes that have excellent performance with reasonable decoding complexity for this channel. Subsequently, we consider the problem of channel state feedback in cellular systems, and model this problem as the transmission of analog sources over a MIMO-MAC (MIMO multiple access channel). We develop a framework for analyzing this problem in terms of minimizing the distortion, and come up with separated source-channel schemes and joint source-channel schemes that perform better than traditional analog feedback. The results are validated through simulations using very simple channel codes.
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