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

Shota Saito, Nozomi Miya, Toshiyasu Matsushima

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2407-2414
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE98A
Issue number12
DOIs
Publication statusPublished - 2015 Dec

Keywords

  • Asymptotic normality
  • Bayes code
  • Law of the iterated logarithm
  • Overflow probability
  • Universal source coding

ASJC Scopus subject areas

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

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