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Personal profile

Research interests

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.

PhD Projects

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.

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Heilbronn Institute

Johnson, O. T.


Project: Research, Parent

Information geometry of graphs

Johnson, O. T.


Project: Research

Research Output

Information theory and the central limit theorem

Johnson, OT., 2004, Imperial College Press. 224 p.

Research output: Book/ReportAuthored book

  • Discrete versions of the transport equation and the Shepp–Olkin conjecture

    Hillion, E. & Johnson, O. T., 2 Feb 2016, In : Annals of Probability. 44, 1, p. 276-306 31 p.

    Research output: Contribution to journalArticle (Academic Journal)

  • 3 Citations (Scopus)
    286 Downloads (Pure)

    Group testing: an information theory perspective

    Aldridge, M., Johnson, O. & Scarlett, J., 5 Dec 2019, In : Foundations and Trends in Communications and Information Theory. 15, 3-4, p. 196-392 196 p.

    Research output: Contribution to journalReview article (Academic Journal)

    Open Access
  • 8 Citations (Scopus)
    51 Downloads (Pure)


    • 14 Media coverage or participation
    • 1 Public talk, debate, discussion

    Quoted in the Observer

    Oliver T Johnson (Interviewee)

    12 Oct 2014

    Activity: Other activity typesMedia coverage or participation

    Quoted in Times report re coronavirus testing

    Oliver T Johnson (Speaker)

    16 Sep 2020

    Activity: Other activity typesMedia coverage or participation

    Interview about coronavirus statistics on BBC Radio 4

    Oliver T Johnson (Speaker)

    6 Aug 2020

    Activity: Other activity typesMedia coverage or participation