Some results on the scalar Gaussian interference channel

We study the optimality of Gaussian signaling (with power control) for the two-user scalar Gaussian interference channel. The capacity region is shown to exhibit a discontinuity of slope around the sum-rate point for a subset of the very weak interference channel. We also show that using colored Gaussians (multi-letter) does not improve on the single-letter region of Gaussian signaling with power control. Finally, we also present an approach to test the optimality of Gaussian signaling motivated by some calculations of the slope of Han-Kobayashi region near the corner point of the Z-interference channel.