khalid sayood introduction data compression solution manual
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#2

Data compression involves the development of a compact
representation of information. Most representations
of information contain large amounts of redundancy.
Redundancy can exist in various forms. It may
exist in the form of correlation: spatially close pixels in
an image are generally also close in value. The redundancy
might be due to context: the number of possibilities
for a particular letter in a piece of English text
is drastically reduced if the previous letter is a q. It can
be probabilistic in nature: the letter e is much more
likely to occur in a piece of English text than the letter
q. It can be a result of how the information-bearing sequence
was generated: voiced speech has a periodic
structure. Or, the redundancy can be a function of the
user of the information: when looking at an image we
cannot see above a certain spatial frequency; therefore,
the high-frequency information is redundant for this
application. Redundancy is defined by the MerriamWebster
Dictionary as “the part of the message that can
be eliminated without the loss of essential information.”
Therefore, one aspect of data compression is redundancy
removal. Characterization of redundancy involves
some form of modeling. Hence, this step in the
compression process is also known as modeling. For
historical reasons another name applied to this process
is decorrelation.
After the redundancy removal process the information
needs to be encoded into a binary representation.
At this stage we make use of the fact that if the
information is represented using a particular alphabet
some letters may occur with higher probability
than others. In the coding step we use shorter code
words to represent letters that occur more frequently,
thus lowering the average number of bits required to
represent each letter.
Compression in all its forms exploits structure, or
redundancy, in the data to achieve a compact representation.
The design of a compression algorithm involves
understanding the types of redundancy present
in the data and then developing strategies for exploiting
these redundancies to obtain a compact representation
of the data. People have come up with
many ingenious ways of characterizing and using the
different types of redundancies present in different
kinds of technologies from the telegraph to the
cellular phone and digital movies.
One way of classifying compression schemes is by
the model used to characterize the redundancy. However,
more popularly, compression schemes are divided
into two main groups: lossless compression and
lossy compression. Lossless compression preserves all
the information in the data being compressed, and
the reconstruction is identical to the original data. In
lossy compression some of the information contained
in the original data is irretrievably lost. The loss in information
is, in some sense, a payment for achieving
higher levels of compression. We begin our examination
of data compression schemes by first looking at
lossless compression techniques.
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