Evaluation of the bayes code from viewpoints of the distribution of its codeword lengths

    研究成果: Article

    2 引用 (Scopus)

    抄録

    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 ∈ (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.

    元の言語English
    ページ(範囲)2407-2414
    ページ数8
    ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    E98A
    発行部数12
    DOI
    出版物ステータスPublished - 2015 12 1

    Fingerprint

    Bayes
    Overflow
    Evaluation
    Source Coding
    Law of the Iterated Logarithm
    End point
    Asymptotic Normality
    Upper and Lower Bounds
    Exceed
    Necessary Conditions
    Sufficient Conditions
    Zero

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Computer Graphics and Computer-Aided Design
    • Applied Mathematics
    • Signal Processing

    これを引用

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    title = "Evaluation of the bayes code from viewpoints of the distribution of its codeword lengths",
    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 ∈ (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.",
    keywords = "Asymptotic normality, Bayes code, Law of the iterated logarithm, Overflow probability, Universal source coding",
    author = "Shota Saito and Nozomi Miya and Toshiyasu Matsushima",
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    N2 - 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 ∈ (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.

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    KW - Asymptotic normality

    KW - Bayes code

    KW - Law of the iterated logarithm

    KW - Overflow probability

    KW - Universal source coding

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