The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of the phase transitions between the various strategies. The Gaussian Z-interference channel with weak interference is known to have two critical points in its capacity region, where the slope of the region shows a sudden change. They occur at the points of the unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. In this paper, we discuss additional critical points (locations of phase transitions) in the achievable region of this channel. These turn out to be second-order phase transitions, i.e., we do not observe a discontinuous slope in the achievable rate region, but there is a discontinuity in the second derivative of the rate contour of the achievable region. This review paper is mainly based on some of our ITA (Information Theory and Applications Workshop, UCSD, San Diego, CA, USA) papers since 2011.

The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of the phase transitions between the various strategies. The Gaussian Z-interference channel with weak interference is known to have two critical points in its capacity region, where the slope of the region shows a sudden change. They occur at the points of the unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. In this paper, we discuss two additional critical points (locations of phase transitions) in the achievable region of this channel. At these points, we do not observe a discontinuous slope in the achievable rate region, but there is a discontinuity in the second derivative of the rate contour of the achievable region. This review paper is mainly based on some of our ITA (Information Theory and Applications Workshop, UCSD, San Diego, CA, USA) papers since 2011.