Low-Resolution Scalar Quantization for Gaussian Sources and Absolute Error

Abstract

This correspondence considers low-resolution scalar quantization for a memoryless Gaussian source with respect to absolute error distortion. It shows that slope of the operational rate-distortion function of scalar quantization is infinite at the point D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> 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