Universal Compression, List Decoding, and Logarithmic Loss

Yanina Shkel, Maxim Raginsky, Sergio Verdu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Universal lossy source coding under the logarithmic loss (log-loss) criterion is studied. Bounds on the rate-redundancy of variable-length universal codes with respect to a family of distributions are derived. These bounds correspond to previously derived bounds on distortion-redundancy of fixed-length coding. The asymptotic behavior of the resulting optimization problem is studied for a family of i.i.d. sources with a finite alphabet size. As is the case with distortion-redundancy, rate-redundancy of memoryless sources is lower bounded by frac k 2log n, where n is the blocklength and k is the number of degrees of freedom in the parameter space. The impact of the distortion constraint is on the constant term: higher allowed distortion effectively reduces the volume of the parameter uncertainty set. In view of previously established connections between lossy variable-length coding under log-loss and compression with list decoding, the bounds derived in this work also apply to variable-length coding with list decoding.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages206-210
Number of pages5
ISBN (Print)9781538647806
DOIs
StatePublished - Aug 15 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2018-June
ISSN (Print)2157-8095

Other

Other2018 IEEE International Symposium on Information Theory, ISIT 2018
CountryUnited States
CityVail
Period6/17/186/22/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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