Monotonicity of Step Sizes of MSE-Optimal Symmetric Uniform Scalar Quantizers

• Published in: IEEE transactions on information theory Vol. 65; no. 3; pp. 1782 - 1792
• Main Authors: Na, Sangsin, Neuhoff, David L.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Counters; Density; generalized gamma densities; Least mean square methods; Mean square error methods; Monotonicity; MSE distortion; optimal step size; Quantization (signal); symmetric uniform quantization
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2018.2867182

For generalized gamma probability densities, this paper studies the monotonicity of step sizes of optimal symmetric uniform scalar quantizers with respect to mean squared-error distortion. The principal results are that for the special cases of Gaussian, Laplacian, two-sided Rayleigh, and gamma densities, optimal step size monotonically decreases when the number of levels N increases by two, and that for any generalized gamma density and all sufficiently large N, optimal step size again decreases when N increases by two. Also, it is shown that for a Laplacian density and sufficiently large N, optimal step size decreases when N increases by just one.