A coding theorem for f-separable distortion measures

Yanina Shkel, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this work we relax the usual separability assumption made in rate-distortion literature and propose f-separable distortion measures, which are well suited to model non-linear penalties. The main insight behind f-separable distortion measures is to define an n-letter distortion measure to be an f-mean of single-letter distortions. We prove a rate-distortion coding theorem for stationary ergodic sources with f-separable distortion measures, and provide some illustrative examples of the resulting rate-distortion functions. Finally, we discuss connections between f-separable distortion measures, and the subadditive distortion measure previously proposed in literature.

Original languageEnglish (US)
Article number111
Issue number2
StatePublished - Feb 1 2018

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering
  • General Physics and Astronomy
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)


  • F-separable distortion measure
  • Rate-distortion function
  • Subadditive distortion measure


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