On the Support of Minimum Mean-Square Error Scalar Quantizers for a Laplacian Source 


Vol. 31,  No. 10, pp. 991-999, Oct.  2006


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  Abstract

This paper shows that the support growth of an optimum (minimum mean square-error) scalar quantizer for a Laplacian density is logarithmic with the number of quantization points. Specifically, it is shown that, for a unit-variance Laplacian density, the ratio of the support-determining threshold of an optimum quantizer to(3/√2)1n(N/2) converges to 1, as the number of quantization points grows. Also derived is a limiting upper bound that says that the optimum support cannot exceed the logarithmic growth by more than a constant. These results confirm the logarithmic growth of the optimum support that has previously been derived heuristically.

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  Cite this article

[IEEE Style]

S. Kim and S. Na, "On the Support of Minimum Mean-Square Error Scalar Quantizers for a Laplacian Source," The Journal of Korean Institute of Communications and Information Sciences, vol. 31, no. 10, pp. 991-999, 2006. DOI: .

[ACM Style]

Seongmin Kim and Sangsin Na. 2006. On the Support of Minimum Mean-Square Error Scalar Quantizers for a Laplacian Source. The Journal of Korean Institute of Communications and Information Sciences, 31, 10, (2006), 991-999. DOI: .

[KICS Style]

Seongmin Kim and Sangsin Na, "On the Support of Minimum Mean-Square Error Scalar Quantizers for a Laplacian Source," The Journal of Korean Institute of Communications and Information Sciences, vol. 31, no. 10, pp. 991-999, 10. 2006.

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pISSN : 1226 - 4717
eISSN : 2287 - 3880