Optimum quantizer performance for a class of non-Gaussian memoryless sources

Abstract

The performance of optimum quantizers subject to an entropy constraint is studied for a wide class of memoryless sources. For a general distortion criterion, necessary conditions are developed for optimality and a recursive algorithm is described for obtaining the optimum quantizer. Under a mean-square error criterion, the performance of entropy encoded uniform quantization of memoryless Gaussian sources is well-known to be within <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.255</tex> bits/sample of the rate-distortion bound at relatively high rates. Despite claims to the contrary, it is demonstrated that similar performance can be expected for a wide range of memoryless sources. Indeed, for the cases considered, the worst case performance is observed to be less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.3</tex> bits/sample from the rate-distortion bound, and in most cases this disparity is less at Iow rates.