Audio Signal Processing and Coding

3.4 VECTOR QUANTIZATION

Data compression via vector quantization (VQ) is achieved by encoding a data-set jointly in block or vector form. Figure 3.11(a) shows an N-dimensional quantizer and a codebook. The incoming vectors can be formed from consecutive data samples or from model parameters. The quantizer maps the i-th incoming [N × 1] vector given by

to a n-th channel symbol u_n, n = 1, 2, … , L as shown in Figure 3.11(a). The codebook consists of L code vectors,

which reside in the memory of the transmitter and the receiver. A vector quantizer works as follows. The input vectors, s_i, are compared to each codeword, , and the address of the closest codeword, with respect to a distortion measure , determines the channel symbol to be transmitted. The simplest and most commonly used distortion measure is the sum of squared errors which is given by

The L[N × 1] real-valued vectors are entries of the codebook and are designed by dividing the vector space into L nonoverlapping cells, c_n, as ...