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 | |
| State | Published - Jul 2008 |
| Externally published | Yes |
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.
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