On the Support of Minimum Mean-Square Error Scalar Quantizers for a Laplacian Source
Seongmin Kim, Sangsin Na · 2006
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 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.