Lagrangian empirical design of variable-rate vector quantizers: consistency and convergence rates

Author

Linder, Tamás

Author_Institution

Dept. of Math. & Stat., Queen´´s Univ., Kingston, Ont., Canada

Volume

48

Issue

11

fYear

2002

fDate

11/1/2002 12:00:00 AM

Firstpage

2998

Lastpage

3003

Abstract

The Lagrangian formulation of variable-rate vector quantization is known to yield useful necessary conditions for quantizer optimality and generalized Lloyd algorithms for quantizer design. The Lagrangian formulation is demonstrated to provide a convenient framework for analyzing the empirical design of variable-rate vector quantizers. In particular, the consistency of empirical design based on minimizing the Lagrangian performance over a stationary and ergodic training sequence is shown for sources with finite second moment. The finite sample performance is also studied for independent training data and sources with bounded support

Keywords

convergence of numerical methods; entropy; sequences; signal sampling; vector quantisation; Lagrangian empirical design; Lagrangian formulation; Lagrangian performance minimization; bounded support; convergence rates; empirical design; entropy-constrained quantization; ergodic training sequence; finite sample performance; finite second moment; generalized Lloyd algorithms; independent training data; independent training sources; quantizer optimality; stationary training sequence; variable-rate vector quantizers; Algorithm design and analysis; Convergence; Councils; Lagrangian functions; Length measurement; Loss measurement; Minimax techniques; Process design; Training data; Vector quantization;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.804114

Filename

1042352