The asymptotic performance of variance-mismatched vector quantizers is presented. It is demonstrated by both asymptotic analysis and computer simulations that well-designed vector quantizers are inherently more invulnerable to mismatch than are conventional scalar quantizers. A generalized exponential density function is considered as a statistical model of sources. As an example, the asymptotic performance is derived and applied to the memoryless Laplacian source with the squared-error distortion measure.

Gersho's bounds on the asymptotic (large rate or small distortion) performance of block quantizers are valid for vector distortion measures that are powers of the Euclidean orl_{2}norm. These results are generalized to difference distortion measures that are increasing functions of the seminorm of their argument, where any seminorm is allowed. This provides ak-dimensional generalization of Gish and Pierce's results for single-symbol quantizers. When the distortion measore is a power of a seminorm the bounds are shown to be strictly better than the corresponding bounds provided by thekth-order rate-distortion functions.

-In this paper a simple expression is derived for the formula of variable quantizing step size. This formula can be used to improve the following ability of the discrete adaptive delta modulation codec. Then it is shown that the previously published formulas for video signal can be reduced to this expression. Next, clarifying the relation between the first-order difference\xiof input signal and the mechanism of appearance of the slope overload noise by using this expression, the quantizing noise is classified into granular noise, the first class slope overload noise and the second class slope overload noise. Then these noises are simply expressed as a function of\xi. Finally, using this result, the signal-to-noise ratios for sinusoidal input and Gaussian input are obtained and in consequence the utility of our simple analytical method is confirmed.