# Vector Quantization

VQ: a generalization of scalar quantization to quantization of a vector

VQ is superior to scalar quantization. Why?

Exploits linear and non-linear dependence that exists among the components of a vector

VQ is superior even when the components of the random vector are statistically independent of each other. How?

A vector quantizer Q of dimension k and size N is a mapping from a vector (or a “point” in Rk), into a finite set C={y1, y2,…, yN}, yiRk, the codebook of size N

Q: RkC

It partitions Rk into N regions or cells, Ri for iJ{1,2,…,N}

Ri={x Rk: Q(x)=yi}