Talk at "International Zurich Seminar on Information and Communication"

Just coming back from Zurich, where I attended the Int. Zurich Seminar. Being there for the fourth time in a row, it felt like a class reunion :). I was speaking about a joint work with Tobi Koch on the information dimension of multivariate Gaussian processes (see below for the slides). The work is on arXiv here and here, and Tobi and I discussed a roadmap for more results to come - stay tuned!

By the way, the IZS publishes its submissions on an ETH server that is free to access for everyone and that does not require to transfer copyrights from the authors to the publisher. This is not only open access at its best, but also gives you a chance to look at the amazing papers presented in Zurich.

"A Rate-Distortion Approach to Caching" Just Got Published!

Our joint work on rate-distortion theory for caching just got published in the IEEE Transactions on Information Theory (it's also available on arXiv, of course; there's also an older post). Thanks Roy, Shirin, and Michele for letting me be a part of this!

In this paper, we consider a lossy single-user caching problem with correlated sources -- just think of streaming compressed videos! Most users will watch these videos in the evening, leading to network congestion. If you have a player with a cache, though, you can fill this cache with data during times of low network usage, even though you may not know which video the user wants to watch in the evening. In our paper, we characterize the transmission rate required in the evening as a function of the cache size and as a function of the distortion one accepts when watching the videos. We furthermore hint at what should be put in the cache such that it is useful for a variety of videos, and we connect these results to the common-information measures proposed by Wyner, Gacs and Koerner.

The picture shows achievable upper (red) and lower converse (black) bounds on the transmission rate as a function of the cache capacity $C$ for doubly symmetric binary source, with the requirement the video is reconstructed perfectly at the receiver. $I(X_1;X_2)$ denotes the mutual information between the two videos, while $K_W(X_1,X_2)$ denotes Wyner's common information.