Stability Analysis of the Gaussian Han-Kobayashi Region for Z-Interference Channels

A major open problem about Z-interference channels is whether the Han-Kobayashi (HK) region with power control is optimal. We analyze the stability of Gaussian stationary points for the HK region, leading to two observations: An inequality conjectured by Costa, Nair, Ng, and Wang (ISIT 2020), posed as a sufficient condition for Gaussian optimality of the HK region, is refuted. This suggests that Gaussian optimality of the HK region, if true, cannot be established directly through this route. Second, we characterize the stability phase transition point, and compare it with the structure of Gaussian optimizers in the HK region (with power control), which reveals that Gaussian optimality of the HK region cannot be refuted by any local (under the L⁸ norm with respect to Gaussian reference measure) perturbation. We propose an amended conjecture, whose validity would imply Gaussian optimality of the Han-Kobayashi bound in a certain regime.Omitted proofs can be found in the full paper [14].