Databases Reference
In-Depth Information
2.0
1.8
1.6
1.4
1.2
msqe
1.0
0.8
0.6
0.4
0.2
0
01 2 3 4
Ratio of input variance to design variance
5
6
789 0
FIGURE 9.12
The
msqe
as a function of variance mismatch with a 4-bit uniform
quantizer.
Notice that as we go from left to right in the table, the designed step size becomes pro-
gressively larger than the “correct” step size. This is similar to the situation where the input
variance is smaller than the assumed variance. As we can see when we have a mismatch
that results in a smaller step size relative to the optimum step size, there is a greater drop in
performance than when the quantizer step size is larger than its optimum value.
9.5 Adaptive Quantization
One way to deal with the mismatch problem is to adapt the quantizer to the statistics of the
input. Several things might change in the input relative to the assumed statistics, including
the mean, the variance, and the
pdf
. The strategy for handling each of these variations can be
different, though certainly not exclusive. If more than one aspect of the input statistics changes,
it is possible to combine the strategies for handling each case separately. If the mean of the
input is changing with time, the best strategy is to use some form of differential encoding
(discussed in some detail in Chapter 11). For changes in the other statistics, the common
approach is to adapt the quantizer parameters to the input statistics.
There are two main approaches to adapting the quantizer parameters: an
offline
or
for-
ward adaptive
approach, and an
online
or
backward adaptive
approach. In forward adaptive
quantization, the source output is divided into blocks of data. Each block is analyzed before
quantization, and the quantizer parameters are set accordingly. The settings of the quantizer
are then transmitted to the receiver as
side information
. In backward adaptive quantization, the
adaptation is performed based on the quantizer output. As this is available to both transmitter
and receiver, there is no need for side information.
