# 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 2407-2414 8 IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98A 12 https://doi.org/10.1587/transfun.E98.A.2407 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

：: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 巻 E98A, 番号 12, 01.12.2015, p. 2407-2414.

研究成果: Article

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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.

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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