Other generalizations

There are several other improvements for this shape-gain quantizer. For example, instead of using a scalar quantizer for the gain, gains could be blocked together and vector quantized, or, if fixed rate quantization is not required, entropy coded. Or, we may remove the assumption that the gain and shape codebooks operate independently. With a gain-dependent shape codebook, there could be a different shape codebook associated with each quantized gain value. With a shape-dependent gain codebook, we could choose $\hat g$ to minimize $\Vert X-\hat g\hat S\Vert$ instead of $\Vert g-\hat g\Vert$.