Vector Quantization - Tools for Signal Compression - page 27

The second ratio represents how vector quantization takes account of the

correlation between the different vector components. When N →∞ , the ratio tends

toward the asymptotic prediction gain value G p ( ∞ ) as shown in equation [1.12].

Figure 2.4 shows the signal-to-noise ratio for vector quantization (as a function of
N ) and for predictive scalar quantization (as a function of P +1)for b =2. The limit
of the signal-to-noise ratio for vector quantization can be seen when N tends toward
infinity. The signal-to-noise ratio for predictive scalar quantization is:

SNR QSP =6 . 02 b − 4 . 35 + 10 log 10 G p ( ∞ )

when P ≥ 2. The 4.35-dB shift between the two horizontal lines is from the ratio

c (1) /c ( ). Vector quantization offers a wide choice in the selection of the geometric

shape of the partition. This explains the gain of 4.35 dB (when N tends toward
infinity).

∞

Vector quantization makes direct use of correlation in the signal. Predictive scalar
quantization also uses this correlation but only after decorrelating the signal.

25

20

15

10

5

Predictive scalar quantization
Vector quantization
Entropy coding with memory

0

2 4 6 8 10 12 14 16 18 20

as a function of N or P+1

Figure 2.4. Signal-to-noise ratio as a function of N for vector quantization
and as a function of P + 1 for predictive scalar quantization