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

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1 Author(s)
Sangsin Na ; Sch. of Electr. & Comput. Eng., Ajou Univ., Suwon, South Korea

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.

Published in:

IEEE Transactions on Information Theory  (Volume:50 ,  Issue: 5 )