Databases Reference
In-Depth Information
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F I GU R E 1 . 3
A sequence of data values.
The type of structure or redundancy that existed in these data follows a simple law. Once
we recognize this law, we can make use of the structure to
predict
the value of each element
in the sequence and then encode the residual. Structure of this type is only one of many types
of structure.
Example1.2.2:
Consider the following sequence of numbers:
27
28
29
28
26
27
29
28
30
32
34
36
38
The sequence is plotted in Figure
1.3
.
The sequence does not seem to follow a simple law as in the previous case. However, each
value in this sequence is close to the previous value. Suppose we send the first value, then
in place of subsequent values we send the difference between it and the previous value. The
sequence of transmitted values would be
27
1
1
-1
-2
1
2
-1
2
2
2
2
2
Like the previous example, the number of distinct values has been reduced. Fewer bits are
required to represent each number, and compression is achieved. The decoder adds each
received value to the previous decoded value to obtain the reconstruction corresponding to the
received value. Techniques that use the past values of a sequence to
predict
the current value
and then encode the error in prediction, or residual, are called
predictive coding
schemes. We
will discuss lossless predictive compression schemes in Chapter 7 and lossy predictive coding
schemes in Chapter 11.
