Vector Quantization

We considered scalar quantization of a scalar source and a vector source. An alternate approach to coding a vector source is to divide the scalars into blocks, view each block as a unit, or a cell, and then jointly quantize the scalars in the unit. This is referred to as vector quantization.In short VQ.

Let denote an N-dimensional vector containing N real valued, continuous amplitude scalars .In vector quantization, is mapped to another N- dimensional vector  where is chosen from L possible reconstruction quantization levels. Let denote that has been quantized i.e . where for denotes L reconstruction levels and is called the  cell. If is in cell is mapped to .

Figure (3.4.1)

An example of vector quantization when N=2 and L=9 is shown in Figure (3.4.1 ).

The filled in dots are reconstruction levels and solid lines are cell boundaries.

Note that a cell can have arbitrary size and shape in vector quantization. While in scalar quantization, cell (region between two consecutive decision levels) can have arbitrary size and shaped shape. Vector quantization exploits this added flexibility.

As in scalar quantization, we define a distortion measure which is a measure of dissimilarity between . An example of  is where quantization noise

is	(3.4.1)

The reconstruction levels and boundaries of cells are determined by minimizing some error criteria such as the average distortion measure given by

	(3.4.2)

If d is then from equation (1) and (2) we get

	(3.4.3)