Exploring Aligned-Images Bounds: Robust Secure GDoF of 3-to-1 Interference Channel

Sum-set inequalities based on Aligned-Images bounds have been recently introduced as essential elements of converse proofs for asymptotic/approximate wireless network capacity characterizations under robust assumptions, i.e., assumptions that limit channel knowledge at the transmitters to finite precision. While these sum-set inequalities have produced robust Generalized Degrees of Freedom (GDoF) results for various wireless networks, their scope and limitations in general are not well understood. To explore these limitations, in this work we study the robust secure GDoF of a symmetric 3-user many-to-one interference channel. We identify regimes where existing sum-set inequalities are sufficient, settling the GDoF for those settings. For the remaining regime we conjecture the form of new sum-set inequalities that may be needed, whose validity remains an open problem for future work.