Rényi information dimension: Fundamental limits of almost lossless analog compression

Yihong Wu, Sergio Verdú

Research output: Contribution to journalArticle

Abstract

In Shannon theory, lossless source coding deals with the optimal compression of discrete sources. Compressed sensing is a lossless coding strategy for analog sources by means of multiplication by real-valued matrices. In this paper we study almost lossless analog compression for analog memoryless sources in an information-theoretic framework, in which the compressor or decompressor is constrained by various regularity conditions, in particular linearity of the compressor and Lipschitz continuity of the decompressor. The fundamental limit is shown to the information dimension proposed by Rnyi in 1959.

Original languageEnglish (US)
Article number5508633
Pages (from-to)3721-3748
Number of pages28
JournalIEEE Transactions on Information Theory
Volume56
Issue number8
DOIs
StatePublished - Aug 1 2010

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Keywords

  • Analog compression
  • Rnyi information dimension
  • Shannon theory
  • compressed sensing
  • information measures
  • source coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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