A simple derivation of Lloyd's classical result for the optimum scalar quantizer (Corresp.)
N. Judell, Louis L. Scharf · IEEE Transactions on Information Theory · 1986
The classical result of Lloyd for the optimum scalar quantizer in the asymptotic case of fine quantization is derived from first principles. The derivation is offered as a simple alternative to Lloyd's original and elegant piece of analysis, and the result is used to derive the optimum compander. We then show why a compander that presents uniformly distributed random variables to the quantizer is not a good idea.