Quantization Distortion in Pulse-Count Modulation with Nonuniform Spacing of Levels

On the Characteristics of MSE-Optimal Symmetric Scalar Quantizers for the Generalized Gamma, Bucklew-Gallagher, and Hui-Neuhoff Sources

“…( 1 2 ) When the second integration term in the bracket is approximated as a Panter-Dite formula-like expression [4] for optimal    , we have …”

“…An asymptotic formula for      , i.e.,   in (1), is provided by the Panter-Dite formula [4] …”

“…In general without actual design it is difficult to estimate accurately thresholds, quantization levels, and the mean-square error (MSE) distortion of an optimal (minimum MSE) quantizer. However, when the number of levels is large, the high resolution quantization theory [4][5][6][7][8][9][10] has discovered approximation formulas that are increasingly accurate with more number of levels for some of such characteristics. This paper extends in particular these two studies [9][10] , respectively, to nonuniform quantizers and to source probability density functions (pdfs) with heavier tails; investigates the uniqueness problem of the differentiation approach [9] for finding optimal step sizes; and assesses accuracies of these formulas by comparing them with those of numerically designed quantizers.…”

Chatting in distributed quantization networks

“…where ≃ indicates that the ratio of the two expressions approaches 1 as K increases [19], [20]. Hence, the MSE performance of a scalar quantizer can be approximated by a simple relationship between the source distribution, point density and codebook size, and this relation becomes more precise with increasing K. Moreover, quantizers designed according to this approximation are asymptotically optimal, meaning that the quantizer optimized over λ has distortion that approaches the performance of the best Q K found by any means [21]- [23].…”

The stochastic quantization method and its application to the numerical simulation of volcanic conduit dynamics under random conditions

“…The origins of the theory of quantization of probability distributions date back to the three fundamental articles (Oliver et al, 1948;Bennett, 1948;Panter and Dite, 1951); the field of application was that of signal processing, in particular modulation and analog-to-digital conversion. See (Gray and Neuhoff, 1998) for a survey of the method and of its engineering applications, besides a huge list of references (mainly in the field of engineering); the book (Graf and Luschgy, 2000) gives a mathematically rigorous treatment of the subject.…”