Low-resolution scalar quantization for Gaussian sources and absolute error
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-max 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.
scalar quantization gaussian absolute error low rate entropy constrained quantization low resolution