Universal covertness for Discrete Memoryless Sources

Remi A. Chou, Matthieu R. Bloch, Aylin Yener

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Consider a sequence S of length n emitted by a Discrete Memoryless Source (DMS) with unknown distribution p. We wish to construct a lossless source code that maps S to a sequence S′ of minimal length m such that S′ approximates in terms of Kullback-Leibler divergence a sequence emitted by another DMS with known distribution q. Our main result is the existence of a coding scheme that performs such a task with an asymptotically optimal compression rate, i.e., such that the limit of m/n is H(p)/H(q) as n goes to infinity. Our coding scheme overcomes the challenges created by the lack of knowledge about p by relying on a sufficiently fine estimation of H(p), followed by an appropriately designed type-based compression that jointly performs source resolvability and universal lossless source coding. Our result recovers several previous results that either assume p uniform, or q uniform, or p known. The price paid for these generalizations is the use of common randomness with vanishing rate. We further determine that the length of the latter roughly scales as the square root of n, by an analysis of second order asymptotics and error exponents.

    Original languageEnglish (US)
    Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages516-523
    Number of pages8
    ISBN (Electronic)9781509045495
    DOIs
    StatePublished - Feb 10 2017
    Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
    Duration: Sep 27 2016Sep 30 2016

    Publication series

    Name54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016

    Other

    Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
    CountryUnited States
    CityMonticello
    Period9/27/169/30/16

    All Science Journal Classification (ASJC) codes

    • Artificial Intelligence
    • Computational Theory and Mathematics
    • Computer Networks and Communications
    • Hardware and Architecture
    • Control and Optimization

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  • Cite this

    Chou, R. A., Bloch, M. R., & Yener, A. (2017). Universal covertness for Discrete Memoryless Sources. In 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 (pp. 516-523). [7852275] (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2016.7852275