High-resolution source coding for non-difference distortion measures: The rate-distortion function

Tamâs Linder*, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The problem of asymptotic (i.e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x,y) -\\W(x)(y -x)\\2, y, x 6 R, the asymptotic expression for the rate-distortion function of X 6 R" at distortion level D equals h(X) - | log (2-KeD/n) + B log |det W(X)\ where h(X) is the differential entropy of X. Extensions to staionary sources and to high-resolution remote ("noisy") source coding are also given. In a companion paper in this issue these results are applied to develop a high-resolution quantization theory for non-difference distortion measures.

Original languageEnglish
Pages (from-to)533-547
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - 1999
Externally publishedYes


  • Asymptotic quantization theory
  • Non-difference distortion measures
  • Rate-distortion function
  • Remote source coding
  • Shannon lower bound


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