Sampling and Quantization - Digital Speech: Coding for Low Bit Rate Communication Systems - page 49

The usefulness of a split vector quantization is in its flexibility in choosing
the dimension of each split part and in the allocation of the overall bits per
input vector to these parts according to the perceptual importance of the
vector elements contained in each split part.

Gain Shape Codebooks
In the earlier discussion of scalar quantization, it was mentioned that the
variance of the input speech signal affected the performance of the quantizer.
This is also true in the case of a vector quantizer. For example, if the input
signal variance is fixed at a certain value, all of the codebook entries will
have the same variance and differ only in the shape of vector elements.
In addition, if we assume that the same number of shape combinations is
repeated with another variance level at the input, the number of codebook
entries would have to be doubled to cover the vector shapes at two different
energy levels. Therefore, if the input vectors have a large dynamic range,
the required codebook size may be too large for practical implementation in
both computation and storage. This problem can be overcome by using the
same idea that is used in scalar quantization: each input vector is normalized
to a certain variance level (usually unity), and then its unit variance shape
is vector quantized using a shape codebook containing candidate vectors
with unity variance. The original variance of the input vector is separately
quantized and transmitted to the de-quantizer for correct scaling. This process
is called gain-shape vector quantization. A block diagram of a gain-shape
vector quantizer is shown in Figure 3.13. The gain of the input vector is
usually calculated and quantized using a scalar quantizer either before or
during the search of the shape codebook.
If the gain of the input vector is to be calculated and quantized before
finding its shape then the quantized gain is calculated as:

N

1
N

x i

σ x = Q (3.63)

i = 1

x(n)

index i

Input Vector
Buffer

x

Match
x and σ i y i

σ i

y i

Codebook

Figure 3.13 Gain-shape vector quantizer