<p>Two coding schemes based on polar codes are proposed for the multiple description (MD) problem. The first scheme is an adaptation of the one developed by \c{S}a\c{s}o\u{g}lu {\em et al.} for the multiple access channel to the MD setting. Specifically, it is shown that the scheme is able to achieve certain rate pairs on the dominant line of the achievable rate region determined by El Gamal and Cover (EGC) when the associated auxiliary random variables have different prime alphabet sizes. Different from polar coding for the multiple access channel considered by \c{S}a\c{s}o\u{g}lu {\em et al.}, the auxiliary random variables in the MD problem can be dependent, and their alphabet sizes play an unexpected important role in the construction. The second scheme is based on the idea of rate splitting. We show that it can achieve the entire EGC rate region. The effectiveness of the proposed polar coding schemes is verified by the experimental results.</p> / Master of Applied Science (MASc)

Multi-User Multi-Input Multi-Output (MU-MIMO) systems are considered to be the sustainable technologies of the current and future of the upcoming wireless and mobile networks generations. The perspectives of these technologies under several scenarios is the focus of the present thesis. The initial system model covers the MU-MIMO, especially in the massive form that is considered to be the promising ideas and pillars of the 5G network. It is observed that the optimal number of users should be served in the time-frequency resource even though the maximum limitation of the MU-MIMO is governed by the total receiving antennas (K) is less than or equal to the base station antennas (M). The system capacity of the massive MIMO (mMIMO) under perfect channel state information (CSI) of uncorrelated channel is investigated and studied. Two types of precoders were applied, one is directly based on channel inversion, and the other uses the Eigen decomposition that is derived subject to the signal to a leakage maximization problem. The two precoders show a degree of equivalency under certain assumptions for the number of antennas at the user end. The convex optimization of multi-antenna networks to achieve the design model of optimum beamformer (BF) based on the uniform linear array (ULA) is studied. The ULA is selected for its simplicity to analyse many scenarios and its importance to match the future network applied millimetre wave (mmWave) spectrum. The maximum beams generated by the ULA are explored in terms of several physical system parameters. The duality between the MU-MIMO and ULA and how they are related based on beamformer operation are detailed and discussed. Finally, two approaches for overloaded systems are presented when the availability of massive array that is not guaranteed due to physical restrictions since the existence of a large number of devices will result in breaking the dimension rule (i.e., K ≤ M). As a solution, a low complexity users selection algorithm is proposed. The channel considered is uncorrelated with full and perfect knowledge at the BS. In particular, these two channel conditions may not be available in all scenarios. The CSI may be imperfect, and even the instantaneous form does not exist. A hybrid precoder between the mixed CSI (includes imperfect and statistical) and rate splitting approach is proposed to deal with an overloaded system under a low number of BS antennas. / Ministry of Higher Education and Scientific Research of Iraq