Universal Lossy Coding for Individual Sequences Based on Complexity Functions

  • Authors:

  • Shigeaki Kuzuoka;Tomohiko Uyematsu

  • Affiliations:

  • The authors are with Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550 Japan. E-mail: kuzuoka@it.ss.titech.ac.jp, E-mail: uyematsu@ieee.org;The authors are with Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550 Japan. E-mail: kuzuoka@it.ss.titech.ac.jp, E-mail: uyematsu@ieee.org

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2007

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Abstract

This paper investigates the fixed-rate and fixed-distortion lossy coding problems of individual sequences subject to the subadditive distortion measure. The fixed-rate and fixed-distortion universal lossy coding schemes based on the complexity of the sequence are proposed. The obtained coding theorems reveal that the optimal distortion (resp. rate) attainable by the fixed-rate (resp. fixed-distortion) lossy coding is equal to the optimal average distortion (resp. rate) with respect to the overlapping empirical distribution of the given sequence. Some connections with the lossy coding problem of ergodic sources are also investigated.