Do optimal entropy-constrained quantizers have a finite or infinite number of codewords?

• Published in: IEEE transactions on information theory Vol. 49; no. 11; pp. 3031 - 3037
• Main Authors: Gyorgy, A., Linder, T., Chou, P.A., Betts, B.J.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Associate members; Codes; Counters; Distortion; Distortion measurement; Entropy; Gaussian; Hulls; Hulls (structures); Information theory; Lagrangian functions; Mathematical analysis; Mathematical models; Mathematics; Optimization; Probability distribution; Quantization; Source coding; Statistics; Theory

An entropy-constrained quantizer Q is optimal if it minimizes the expected distortion D(Q) subject to a constraint on the output entropy H(Q). We use the Lagrangian formulation to show the existence and study the structure of optimal entropy-constrained quantizers that achieve a point on the lower c...