Achieving the Gaussian rate-distortion function by prediction

Ram Zamir*, Yuval Kochman, Uri Erez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


The "water-filling" solution for the quadratic rate-distortion function of a stationary Gaussian source is given in terms of its power spectrum. This formula naturally lends itself to a frequency domain "test-channel"realization. We provide an alternative time-domain realization for the rate-distortion function, based on linear prediction. The predictive test channel has some interesting implications, including the optimality at all distortion levels of pre/post filtered vector-quantized differential pulse-code modulation (DPCM), and a duality relationship with decision-feedback equalization (DFE) for intersymbol interference (ISI) channels.

Original languageAmerican English
Pages (from-to)3354-3364
Number of pages11
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2008
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received July 27, 2006; revised December 19, 2007. The work of R. Zamir and Y. Kochman was supported in part by the Israel Science Foundation under Grant ISF 1259/07. The work of U. Erez was supported in part by the Israel Science Foundation under Grant ISF 1234/06. The material in this correspondence was presented in part at IEEE International Symposium on Information Theory, Seattle, WA, July 2006.


  • Decision feedback
  • Differential pulse-code modulation (DPCM)
  • Directed-information
  • Entropy coded dithered quantization (ECDQ)
  • Equalization
  • Minimum mean-square error (MMSE) estimation
  • Pre/post-filtering
  • Shannon lower bound
  • Test channel
  • Water-filling


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