Necessary conditions for the optimality of variable-rate residual vector quantizers

-Residual vector quantizatlon (RVQ), or multistage VQ, as it is also called, has recently been shown to be a competitive technique for data compression [1]. The competitive performance of RVQ reported in [1] results from the joint optimization of variable rate encoding and RVQ direct-sum codebooks. In this paper, necessary conditions for the optimality of variable rate RVQs are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing RVQs having minimum average distortion subject to an entropy constraint. Simulation results for these entropy-constrained RVQs (EC-RVQs) are presented for memoryless Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The performance is superior to that of entropy-constrained scalar quantizers (EC-SQs) and practical entropy-constrained vector quantizers (EC-VQs), and is competitive with that of some of the best source coding techniques that have appeared in the literature. lndez Terms--Residual vector quantization, multistage vector quantization, entropy, source coding. "This work was supported in part by the National Science Foundation under contract MIP9116113 and by NASA.