Minimum expected distortion in Gaussian source coding with fading side information

Chris T.K. Ng, Chao Tian, Andrea J. Goldsmith, Shlomo Shamai

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared-error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

Original languageEnglish (US)
Article number6216424
Pages (from-to)5725-5739
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Convex optimization
  • Heegard-Berger
  • distortion minimization
  • fading channel
  • rate-distortion function
  • side information
  • source coding


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