A Lagrangian formulation of high rate quantization

The asymptotic optimal performance of variable-rate vector quantizers of fixed dimension and large rate was first developed in a rigorous fashion by Paul Zador (1966). Subsequent design algorithms for such compression codes used a Lagrangian formulation in order to generalize Lloyd's classic quantizer optimization algorithm to variable rate codes. This formulation has been subsequently adopted in a variety of practical systems including rate-optimized streaming video. We describe a Lagrangian formulation of Zador's variable-rate quantization results and apply it to estimate Zador's constant using the generalized Lloyd algorithm.