Evaluation of the Bayes Code from Viewpoints of the Distribution of Its Codeword Lengths

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Author(s)

    • SAITO Shota
    • Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University
    • MIYA Nozomi
    • Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University
    • MATSUSHIMA Toshiyasu
    • Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University

Abstract

This paper considers universal lossless variable-length source coding problem and investigates the Bayes code from viewpoints of the distribution of its codeword lengths. First, we show that the codeword lengths of the Bayes code satisfy the asymptotic normality. This study can be seen as the investigation on the asymptotic shape of the distribution of codeword lengths. Second, we show that the codeword lengths of the Bayes code satisfy the law of the iterated logarithm. This study can be seen as the investigation on the asymptotic end points of the distribution of codeword lengths. Moreover, the overflow probability, which represents the bottom of the distribution of codeword lengths, is studied for the Bayes code. We derive upper and lower bounds of the infimum of a threshold on the overflow probability under the condition that the overflow probability does not exceed ε∈(0,1). We also analyze the necessary and sufficient condition on a threshold for the overflow probability of the Bayes code to approach zero asymptotically.

Journal

  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98.A(12), 2407-2414, 2015

    The Institute of Electronics, Information and Communication Engineers

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