On embedded scalar quantization

The paper studies the rate-distortion performance of symmetric scalar quantizers having a large (effectively infinite) number of steps and using the same step size for all steps except the one containing the zero input value. Quantizers of this form have been shown to have good performance for a variety of sources, and are precisely optimal for the Laplacian source. The performance is investigated particularly for embedded quantization, in which the representation of a source quantity is refined successively by forming finer quantizers from further segmentation of the steps of coarser quantizer constructions. Although the use of a double-wide dead-zone has dominated prior embedded quantization practice, it is shown that any rational number can be maintained as a stable dead-zone ratio. Two forms are investigated in more depth - quantizers with dead-zone ratios of 1 and 2 - and a ratio of 1 is shown often to provide a significant performance advantage (up to 1 dB). Performance is explored primarily in the context of the generalized Gaussian pdf using the squared-error distortion measure, but should also apply in other contexts.