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

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