Sum Capacity of Degraded Gaussian Interference Networks

This paper determines the sum-capacity of degraded Gaussian K-user interference channels (IFCs). To this end, the paper first develops a family of genie-MAC (multiple access channel) outer bounds for Gaussian K-user interference channels. This family is based on existing genie-aided bounding mechanisms, but differs from current approaches in its optimization problem formulation and application. The genie-aided bound (based on [2]) creates a group of genie receivers that form multiple access channels (MACs) that can decode a subset of the original IFC’s messages. The MAC sum-capacity of each of the genie receivers provides an outer bound on the sum of rates for this subset. This genieaided MAC bound is formulated as an optimization problem, whose solution is shown to be tight in sum-capacity for the degraded Gaussian K-user IFC. The scheme that achieves sum-capacity is shown to be successive interference cancellation. Next, the paper generalizes its framework to unit-rank interference channels where each user is equipped with multiple antennas. Again, the sum-capacity of the MIMO unit-rank Gaussian IFC is characterized in this paper using a combination of a optimization problem resulting from a genie-aided outer bound and successive interference cancellation as the achievable scheme. The proof in the MIMO case establishes an equivalence between the MIMO unit-rank K-user IFC and a corresponding SISO degraded K-user IFC.