Embedded max quantization

The Max quantizer is a well-known algorithm for accomplishing efficient approximate representation of analog samples from a signal source by using values taken from a finite set of allowed values when the probability density function of the source is known. In some applications, it is desired to have embedded quantization that allows successively better approximation to the input sample when additional information bits become available. The Max quantizer lacks this feature. In this paper, we propose a method to achieve embedded quantization by iteratively aligning the quantization thresholds of an i-bit quantizer with those of an (i + 1)-bit quantizer and optimizing the finer thresholds and reconstruction levels. The designed quantizers achieve a mean square quantization error almost as low as that achieved by the Max quantizers.