Given h<0, the problem is considered of finding an N-level quantizer Q which is optimal in the sense of encoding a given continuously distributed random variable X with minimum expected squared error, subject to the constraint H(Q(X))>or=h on the entropy H(Q(X)) of the quantizer output Q(X). Results are given on the existence and uniqueness of optimal entropy-constrained quantizers. An efficient algorithm is given that starts with an initial quantizer and generates a sequence of quantizers that converges to an optimal entropy-constrained quantizer for a wide class of distributions of X.
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