On the support of fixed-rate minimum mean-squared error scalar quantizers for a Laplacian source

Authors:
Sangsin Na
Affiliations:
Sch. of Electr. & Comput. Eng., Ajou Univ., Suwon, South Korea
Venue:
IEEE Transactions on Information Theory
Year:
2004

Citing 0
Cited 4

Optimal designing scalar quantizers using a hybrid quantization method for the laplacian source

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Abstract

This correspondence shows that the support growth of a fixed-rate optimum (minimum mean-squared 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/√2lnN/2 converges to 1, as the number N of quantization points grows. Also derived is a limiting upper bound that says that the support-determining threshold cannot exceed the logarithmic growth by more than a small constant, e.g., 0.0669. These results confirm the logarithmic growth of the optimum support that has previously been derived heuristically.