Databases Reference
In-Depth Information
9.6 Nonuniform Quantization
As we can see fromFigure
9.10
, the input is more likely to fall in the inner levels of the quantizer
if the input distribution has more mass near the origin. Recall that in lossless compression, in
order to minimize the
average
number of bits per input symbol, we assigned shorter codewords
to symbols that occurredwith higher probability and longer codewords to symbols that occurred
with lower probability. In an analogous fashion we can try to approximate the input better
in regions of high probability, perhaps at the cost of worse approximations in regions of
lower probability, in order to decrease the average distortion. We can do this by making the
quantization intervals smaller in those regions that have more probability mass. If the source
distribution is like the distribution shown in Figure
9.10
, we would have smaller intervals near
the origin. If we wanted to keep the number of intervals constant, this would mean we would
have larger intervals away from the origin. A quantizer that has nonuniform intervals is called
a
nonuniform quantizer
, an example of which is shown in Figure
9.19
.
Output
y
8
y
7
y
6
y
5
Input
b
1
b
2
b
3
b
4
b
5
b
6
b
7
y
4
y
3
y
2
y
1
F I GU R E 9 . 19
A nonuniform midrise quantizer.
