Databases Reference
In-Depth Information
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Distortion
F I GU R E 8 . 6
The rate distortion function for a Gaussian random variable with vari-
ance 1.
In this section, we have defined the rate distortion function and obtained the rate distortion
function for two important sources. We have also obtained upper and lower bounds on the
rate distortion function for an arbitrary
iid
source. These functions and bounds are especially
useful when we want to know if it is possible to design compression schemes to provide a
specified rate and distortion given a particular source. They are also useful in determining the
amount of performance improvement that we could obtain by designing a better compression
scheme. In these ways, the rate distortion function plays the same role for lossy compression
that entropy plays for lossless compression.
8.6 Models
As in the case of lossless compression, models play an important role in the design of lossy
compression algorithms; there are a variety of approaches available. The set of models we can
draw on for lossy compression is much wider than the set of models we studied for lossless
compression. We will look at some of these models in this section. What is presented here is
by no means an exhaustive list of models. Our only intent is to describe those models that will
be useful in the following chapters.
8.6.1 Probability Models
An important method for characterizing a particular source is through the use of probability
models. As we shall see later, knowledge of the probability model is important for the design
of a number of compression schemes.
