Rényi information dimension: Fundamental limits of almost lossless analog compression

Yihong Wu, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

129 Scopus citations


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
Issue number8
StatePublished - Aug 2010

All Science Journal Classification (ASJC) codes

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


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


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