Signal-to-Noise Ratio Formulas of a Scalar Gaussian Quantizer Mismatched to a Laplacian Source

- Journal title : The Journal of Korean Institute of Communications and Information Sciences
- Volume 36, Issue 6C, 2011, pp.384-390
- Publisher : The Korean Institute of Communications and Information Sciences
- DOI : 10.7840/KICS.2011.36C.6.384

Title & Authors

Signal-to-Noise Ratio Formulas of a Scalar Gaussian Quantizer Mismatched to a Laplacian Source

Rhee, Ja-Gan; Na, Sang-Sin;

Rhee, Ja-Gan; Na, Sang-Sin;

Abstract

The paper derives formulas for the mean-squared error distortion and resulting signal-to-noise (SNR) ratio of a fixed-rate scalar quantizer designed optimally in the minimum mean-squared error sense for a Gaussian density with the standard deviation when it is mismatched to a Laplacian density with the standard deviation . The SNR formulas, based on the key parameter and Bennett's integral, are found accurate for a wide range of . Also an upper bound to the SNR is derived, which becomes tighter with increasing rate R and indicates that the SNR behaves asymptotically as dB.

Keywords

Gaussian Quantizer;Laplacian source;the mean-squared error distortion;shape mismatch;SNR formulas;

Language

English

References

1.

P. F. Panter and W. Dite, "Quantization distortion in pulse count modulation with nonuniform spacing of levels," Proc. IRE, pp. 44-48, Jan. 1951.

2.

S. Na, "Asymptotic formulas for mismatched minimum MSE Laplacian quantizers," IEEE Signal Processing Letters, Vol.15, pp.13-16, Jan. 2008.

3.

S. Na and D. L. Neuhoff, "On the support of MSE-optimal, fixed-rate, scalar quantizers," IEEE Trans. Inform. Thy., Vol.IT-47, pp.2972-2982, Nov. 2001.

4.

5.

F. G. Lether and P. R. Wenston, "Elementary approximations for Dawson's integral," J. Quant. Spectrosc. Radiat. Transfer, Vol.46, No. 4, pp.343-345, 1991.

6.

P. O. Borjesson and C.-E. W. Sundberg, "Simple approximations of the error function Q(x) for communications applications," IEEE Trans. Commun., vol. COM-27, pp.639-643, Mar. 1979.

7.

S. Lloyd, "Least squares quantization in PCM," Bell Labs Tech. Note. Portions presented at the Inst. of Math. Stat's Meet., Atlantic City, NJ, Sept. 1957. Also, IEEE Trans. Inform. Thy., Vol.IT-28, pp.129-137, Mar. 1982.

8.

J. Max, "Quantizing for minimum distortion," IRE Trans. Inform. Thy., Vol.IT-6, pp.7-12, Mar. 1960.