Robust Optimality of Secure TIN

In order to discover larger networks and parameter regimes where sharp Generalized Degrees of Freedom (GDoF) characterizations may be found based on the optimality of robust schemes for interference and broadcast networks with channel state information at the transmitters (CSIT) limited to finite precision, we explore the impact of secrecy constraints. In the absence of secrecy constraints, the largest such parameter regime for K user interference networks is the CTIN regime (so named for the C onvexity of the GDoF region achieved by Treating Interference as Noise (TIN)) originally discovered by Yi and Caire, whose optimality was established by Chan et al. For the corresponding broadcast networks the largest regime is the SLS (Simple Layered Superposition) regime discovered by Davoodi and Jafar, but only for small networks with K\leq 3 users. By including secrecy constraints, we identify much larger regimes, the STIN regime and the SLS regime, where GDoF are fully characterized for arbitrary number of users under finite precision CSIT, for interference networks and broadcast networks, respectively. The optimal achievable scheme in both cases is based on TIN along with power control and jamming. Proofs of optimality rely on a combination of secrecy constraints and Aligned Images sum-set inequalities.