Conditional entropy-constrained vector quantization: high-rate theory and design algorithms

• Published in: IEEE transactions on information theory Vol. 41; no. 4; pp. 901 - 916
• Main Authors: de Garrido, D.P., Pearlman, W.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.1995; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Clustering algorithms; Constraint theory; Entropy; Exact sciences and technology; Information technology; Information, signal and communications theory; Nearest neighbor searches; Network address translation; Probability density function; Rate-distortion; Sampling, quantization; Signal and communications theory; Systems engineering and theory; Telecommunications and information theory; Vector quantization; Cluster analysis; Algorithms; Vector quantization; Coding; Entropy; Performance; Optimization; Information theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.391238

The performance of optimum vector quantizers subject to a conditional entropy constraint is studied. This new class of vector quantizers was originally suggested by Chou and Lookabaugh (1990). A locally optimal design of this kind of vector quantizer can be accomplished through a generalization of the well-known entropy-constrained vector quantizer (ECVQ) algorithm. This generalization of the ECVQ algorithm to a conditional entropy-constrained is called CECVQ, i.e., conditional ECVQ. Furthermore, we have extended the high-rate quantization theory to this new class of quantizers to obtain a new high-rate performance bound. The new performance bound is compared and shown to be consistent with bounds derived through conditional rate-distortion theory. A new algorithm for designing entropy-constrained vector quantizers was introduced by Garrido, Pearlman, and Finamore (see IEEE Trans. Circuits Syst. Video Technol., vol.5, no.2, p.83-95, 1995), and is named entropy-constrained pairwise nearest neighbor (ECPNN). The algorithm is basically an entropy-constrained version of the pairwise nearest neighbor (ECPNN) clustering algorithm of Equitz (1989). By a natural extension of the ECPNN algorithm we develop another algorithm, called CECPNN, that designs conditional entropy-constrained vector quantizers. Through simulation results on synthetic sources, we show that CECPNN and CECVQ have very close distortion-rate performance.< >