Non-Asymptotic Bounds and a General Formula for the Rate-Distortion Region of the Successive Refinement Problem

• MATSUTA Tetsunao

  Dept. of Information and Communications Engineering, Tokyo Institute of Technology

• UYEMATSU Tomohiko

  Dept. of Information and Communications Engineering, Tokyo Institute of Technology

Abstract

In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by one of two codewords, and the other reconstruction is obtained by all two codewords. For this coding problem, we give non-asymptotic inner and outer bounds on pairs of numbers of codewords of two encoders such that each probability that a distortion exceeds a given distortion level is less than a given probability level. We also give a general formula for the rate-distortion region for general sources, where the rate-distortion region is the set of rate pairs of two encoders such that each maximum value of possible distortions is less than a given distortion level.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E101.A (12), 2110-2124, 2018-12-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• general source
• information spectrum
• non-asymptotic bound
• rate-distortion region
• successive refinement

Details

• CRID: 1390564238049454464
• NII Article ID: 130007539071
• DOI: 10.1587/transfun.e101.a.2110
• ISSN: 17451337
• ISSN: 09168508
• Web Site: http://t2r2.star.titech.ac.jp/cgi-bin/publicationinfo.cgi?q_publication_content_number=CTT100788554
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E101.A/12/E101.A_2110/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed