We establish the noiseberg conjecture regarding the Han-Kobayashi region of the Gaussian Z-Interference channel with Gaussian signaling. We also provide a refined conjecture for the optimality of the HK inner bound with Gaussian signaling.

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.

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. As corollaries of this inequality, we obtain new results and generalizations and new proofs of known results.

We establish an information inequality that is motivated by the capacity region computation for the Gaussian Z-interference channel. This yields an improved slope for the capacity region at Costa's corner point. We believe the inequality may also be of independent interest as it provides a non-trivial upper bound on the entropy of sums of independent random variables.

In this paper we establish that a maximizer of a non-convex problem in positive semidefinite matrices has a certain property using information-theoretic methods. Further, we propose a Gaussian extremality conjecture, which if true, would imply that Gaussian signaling achieves the capacity region of the Gaussian Z-interference channel. The non-convex problem mentioned above arose naturally in the reduction from the conjecture to the optimality of Gaussian signaling.

A structured code that improves the previously best known exponential asymptotic lower bound for the maximum cardinality of a pairwise-colliding set of permutations is presented. The main contribution is an explicit construction of an infinite recursion of pairwise-colliding sets of partial-permutations.

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.