On the optimality of treating interference as noise: A combinatorial optimization perspective

For single-antenna Gaussian interference channels, we re-formulate the problem of determining the Generalized Degrees of Freedom (GDoF) region achievable by treating interference as noise (TIN) with proper power control from a combinatorial optimization perspective. We show that the TIN power control problem can be cast into an assignment problem, such that the globally optimal power allocation variables can be obtained by well-known polynomial time algorithms. Furthermore, the expression of the TIN-achievable GDoF region can be substantially simplified with the aid of maximum weighted matchings. In addition, we provide conditions under which the TIN-achievable GDoF region is a convex polytope that relax those in [1]. For these new conditions, together with a channel connectivity (i.e., interference topology) condition, we can prove GDoF optimality for a new class of interference networks that is not included, nor includes, the class found in [1].