UC Irvine

The emergence of ‘Aligned Images Sum-set (AIS) Inequalities’ has spurred much progress in Generalized Degrees of Freedom (GDoF) characterizations of wireless networks under robust assumptions that limit the channel state information at transmitters (CSIT). Much of this progress is limited to small networks, and to larger networks under highly symmetric parameter values. Extending these results to larger networks with asymmetric parameters is challenging because of the inherent curse of dimensionality, and also because the scope of AIS bounds is far from well understood. Making progress in this direction is the main goal of this dissertation.We first explore the feasibility of an extremal network theory, i.e., a study of extremal networks within particular parameter regimes of interest. In particular, we quantify the extremal gain in sum GDoF brought about by transmitter cooperation in K user interference channels in various parameter regimes that correspond to weak interference. Specifically, with the robust scheme of ‘Treating Interference as Noise (TIN)’ as the baseline, we find the extremal gain in a large parameter regime (known as the Simple Layered Superposition, or SLS, regime) to be Θ(log2 K), which scales logarithmically with the number of users. As our next contribution we explore robust GDoF characterizations for large networks in the presence of security constraints. We identify surprisingly broad new regimes for both interference and broadcast networks, where robust secure GDoF are fully characterized for arbitrary number of users. The unifying feature of these regimes is the optimality of TIN along with wiretap coding, power control and jamming. Continuing with the security constraint, in the final part of this dissertation we study the robustness of structured codes for secure GDoF characterizations under limited CSIT. In particular, structured jamming based on lattice codes is known to offer significant advantages by allowing receivers to decode and remove the sum of jamming and message signals in aggregate. However, we show that such advantages are completely lost in GDoF under the robust assumption of limited CSIT. The complete robust GDoF characterization of 2 user secure Z channels comes as a byproduct of the analysis. Limitations of existing AIS bounds are identified that stand in the way of generalizations to larger networks in this case.