TY - JOUR

T1 - Evaluation of the bayes code from viewpoints of the distribution of its codeword lengths

AU - Saito, Shota

AU - Miya, Nozomi

AU - Matsushima, Toshiyasu

N1 - Publisher Copyright:
Copyright © 2015 The Institute of Electronics, Information and Communication Engineers.

PY - 2015/12

Y1 - 2015/12

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.

AB - 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.

KW - Asymptotic normality

KW - Bayes code

KW - Law of the iterated logarithm

KW - Overflow probability

KW - Universal source coding

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U2 - 10.1587/transfun.E98.A.2407

DO - 10.1587/transfun.E98.A.2407

M3 - Article

AN - SCOPUS:84948702405

VL - E98A

SP - 2407

EP - 2414

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 12

ER -