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In this paper, the Lagrangian formulation of variable-rate vector quantization is extended to quantization with simultaneous constraints on entropy and codebook size, including variable- and fixed-rate quantization as special cases. The formulation leads to a Lloyd quantizer design algorithm and generalizations of Gersho's approximations characterizing optimal performance for asymptotically large rate. A variation of Gersho's approach is shown to yield rigorous results partially characterizing the asymptotically optimal performance.
Date of Publication: May 2008