When optimal entropy-constrained quantizers have only a finite number of codewords

Philip A. Chou and Bradley J. Betts

January 1998

An entropy-constrained quantizer Q is optimal if it minimizes the expected distortion Ed(X, Q(X)) subject to a constraint on the output entropy H(Q(X)). In general, such an optimal entropy-constrained quantizer may have a countably infinite number of codewords. In this short paper, we show that if the tails of the distribution of X are sufficiently light (with respect to the distortion measure), then the optimal entropy-constrained quantizer has only a finite number of codewords. In particular, for the squared error distortion measure, if the tails of the distribution of X are lighter than the tails of a Gaussian distribution, then the optimal entropy-constrained quantizer has only a finite number of codewords.

Publication type | Inproceedings |

Published in | Int'l Symp. on Information Theory |

Publisher | Institute of Electrical and Electronics Engineers, Inc. © 1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. |

> Publications > When optimal entropy-constrained quantizers have only a finite number of codewords