Codecell convexity in optimal entropy-constrained vector quantization

Properties of optimal entropy-constrained vector quantizers (ECVQs) are studied for the mean squared error (MSB) distortion measure. It is known that restricting an ECVQ to have convex codecells may preclude its optimality for some sources with discrete distribution and show that for sources with continuous distribution, any finite-level ECVQ can be replaced by another finite-level ECVQ with convex codecells that has equal or better performance. This paper also considers the problem of existence of optimal ECVQs for continuous source distributions.