Achieving the Gaussian rate-distortion function by prediction

Ram Zamir; Yuval Kochman; Uri Erez

doi:10.1109/TIT.2008.924683

Achieving the Gaussian rate-distortion function by prediction

Ram Zamir^*, Yuval Kochman, Uri Erez

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	3354-3364
Number of pages	11
Journal	IEEE Transactions on Information Theory
Volume	54
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2008.924683
State	Published - Jul 2008

Keywords

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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10.1109/TIT.2008.924683

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title = "Achieving the Gaussian rate-distortion function by prediction",

abstract = "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.",

keywords = "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",

author = "Ram Zamir and Yuval Kochman and Uri Erez",

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.",

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AU - Kochman, Yuval

AU - Erez, Uri

N1 - 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.

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N2 - 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.

AB - 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.

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KW - Entropy coded dithered quantization (ECDQ)

KW - Equalization

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KW - Pre/post-filtering

KW - Shannon lower bound

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Achieving the Gaussian rate-distortion function by prediction

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