## Bennett's Integral for Vector Quantizers (1995)

Venue: | IEEE Trans. Inform. Theory |

Citations: | 32 - 6 self |

### BibTeX

@ARTICLE{Na95bennett'sintegral,

author = {Sangsin Na and David L. Neuhoff},

title = {Bennett's Integral for Vector Quantizers},

journal = {IEEE Trans. Inform. Theory},

year = {1995},

volume = {41},

pages = {886--900}

}

### OpenURL

### Abstract

This paper extends Bennett's integral from scalar to vector quantizers, giving a simple formula that expresses the rth-power distortion of a many-point vector quantizer in terms of the number of points, point density function, inertial profile and the distribution of the source. The inertial profile specifies the normalized moment of inertia of quantization cells as a function of location. The extension is formulated in terms of a sequence of quantizers whose point density and inertial profile approach known functions as the number of points increases. Precise conditions are given for the convergence of distortion (suitably normalized) to Bennett's integral. Previous extensions did not include the inertial profile and, consequently, provided only bounds or applied only to quantizers with congruent cells, such as lattice and optimal quantizers. The new version of Bennett's integral provides a framework for the analysis of suboptimal structured vector quantizers. It is shown how the loss...