On codecell convexity of optimal multi-resolution scalar quantizers for continuous sources
András Antos
IEEE Transactions on Information Theory 2009. ISSN 0018-9448

Abstract

It has been shown by earlier results that codecell convexity may preclude optimality for multiple-description and for multi-resolution scalar quantizers (MRSQ). Given that the later result is proved showing a discrete counter-example, it could be suspected that for the class of sources with uniformly bounded continuous densities, there is always a convex optimal MRSQ. Here it is shown that this is not so, proving that convexity of fixed-rate MRSQs may preclude optimality also for these subclasses.

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