Professor Oliver Johnson
I am a mathematician, trying to understand randomness. This takes place both through theoretical calculations and through collaborative interdisciplinary work with applied researchers such as engineers and computer scientists.
Professor of Information TheorySchool of Mathematics
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I work on problems at the boundary of probability theory, statistics and information theory.
I have recently been working on the group testing problem. This is a combinatorial search problem, which acts as a prototype of a wider class of sparse inference problems in estimation and statistics. I have developed the idea of rate and capacity of algorithms, and proved a range of theoretical performance guarantees for them in this sense. I am also interested in the idea of converse bounds: that is to show what performance is optimal. This has included recent work to extend the standard Fano-based bounds in statistical inference problems to a sharper criterion based on Renyi entropy.
I am interested in the relationship between properties of entropy and limit theorems, such as the Central Limit Theorem and Law of Small Numbers (Poisson convergence). This includes trying to understand relationships between information-theoretic properties such as the Entropy Power Inequality and maximum entropy theorems and probabilistic ideas such as log-Sobolev inequalities and transportation of measure. I have a particular interest in developing discrete analogues of these results.
I also work on more applied problems relating to communications. I have a particular interest in characterizing `best possible' performance of algorithms or communication schemes, using information-theoretic ideas. This includes an interest in interference mitigation schemes such as Interference Alignment, and spectrum sensing as an application of group testing.
All the topics mentioned above can potentially lead into research projects (with almost no pre-requisites), and I would be happy to discuss them by email with any potential applicant.
My more applied work includes links with Electrical Engineering and Computer Science, and I am happy to participate in other interdisciplinary projects.
01/09/2011 to 01/09/2013
01/07/2010 to 01/01/2011
01/06/2009 to 01/06/2011
01/10/2005 to 30/09/2030
Information theory and the central limit theorem
- Authored book
Annals of Probability
Foundations and Trends in Communications and Information Theory
2023 IEEE Wireless Communications and Networking Conference (WCNC)
- Conference contribution
Journal of Applied Probability
- Accepted/In press
- Authored book
- Conference paper
Probability in the Engineering and Informational Sciences
- E-pub ahead of print