We establish that the multi-letter extension of the Han–Kobayashi achievable region with temporally correlated vector Gaussian inputs matches the Han–Kobayashi achievable region with scalar Gaussian inputs for the Gaussian interference channel.

In this paper we derive an inequality relating linear combinations of mutual information between subsets of mutually independent random variables and an auxiliary random variable. One choice of a family of auxiliary variables leads to a new proof of a Stam-type inequality regarding the Fisher Information of sums of independent random variables. Another choice of a family of auxiliary random variables leads to new results as well as new proofs of results relating to strong data processing constants and maximal correlation between sums of independent random variables. Other results obtained include convexity of Kullback–Leibler divergence over a parameterized path along pairs of binomial and Poisson distributions, as well as a new duality-based argument relating the Stam-type inequality and entropy power inequality.

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.