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

Necessary conditions for the optimality of variable-rate residual vector quantizers are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing residual vector quantizers having minimum average distortion subject to an entropy constraint. Simulation results for entropy-constrained residual vector quantizers are presented for memoryless Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The rate-distortion performance is shown to be competitive with that of entropy-constrained vector quantization and entropy-constrained trellis-coded quantization.