Asymptotical Optimality of Two Variations of Lempel-Ziv Codes for Sources with Countably Infinite Alphabet

  • Authors:

  • Tomohiko Uyematsu;Fumio Kanaya

  • Affiliations:

  • The author is with the Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550 Japan. E-mail: uematsu@it.ss.titech.ac.jp,;The author was with the Faculty Department of Information Science, Shonan Institute of Technology, Fujisawa-shi, 251-0046 Japan.

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2006

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Abstract

This paper considers the universal coding problem for stationary ergodic sources with countably infinite alphabets. We propose modified versions of LZ77 and LZ78 codes for sources with countably infinite alphabets. Then, we show that for any source μ with Eμ[log X1]