While statistical inference and information theory are deeply related fields, problems which lie at the intersection of both disciplines usually fall between the two stools, and lack definitive answers. In this talk, I will discuss recent advances in two such problems.

In the first part of the talk, I will discuss a distributed hypothesis testing problem, in which the hypotheses regard the joint statistics of two sequences, one available to the decision function directly (as side information), while the other is conveyed through a limited-rate link. The goal is to design a system which obtains the optimal trade-off between the false-alarm and misdetection exponents. I will define a notion of "channel detection codes", and show that the optimal exponents of the distributed hypothesis testing problem is directly related to the exponents of these codes. Then, I will discuss a few bounds on the exponents of channel detection codes, as well as prospective improvements. This approach has a two merits over previous works: It is suitable for any pair of memoryless joint distributions, and it provides bounds on the entire false-alarm/misdetection curve, rather than just bounds on its boundary points (Stein's exponent).

In the second part of the talk (time permitting), I will discuss a parameter estimation problem over an additive Gaussian noise channel with bandlimited input. In case one is allowed to design both the modulator and the estimator, the absolute \$alpha$-th moment of the estimation error can decrease exponentially with the transmission time. I will discuss several new upper (converse) bounds for the optimal decrease rate.

Joint work with Yuval Kochman (Hebrew university) and Neri Merhav (Technion).

The Information Theory Forum (IT-Forum) at Stanford ISL is an interdisciplinary academic forum which focuses on mathematical aspects of information processing. With a primary emphasis on information theory, we also welcome researchers from signal processing, learning and statistical inference, control and optimization to deliver talks at our forum. We also warmly welcome industrial affiliates in the above fields. The forum is typically held in Packard 202 every Friday at 1:00 pm during the academic year.

The Information Theory Forum is organized by graduate students Jiantao Jiao and Yanjun Han. To suggest speakers, please contact any of the students.