Low Rate Scalar Quantization for Gaussian Sources and Absolute Error

Abstract

This paper considers low resolution scalar quantization for a memoryless Gaussian source with respect to absolute error distortion. It shows that slope of the the operational rate-distortion function of scalar quantization is infinite at the point Dmax where the rate becomes zero. Thus, unlike the situation for squared error distortion, or for Laplacian and exponential sources with squared or absolute error distortion, for a Gaussian source and absolute error, scalar quantization at low rates is far from the Shannon rate-distortion function, i.e. far from the performance of the best lossy coding technique.