Basic Concepts in Data Compression
In this section the basic concepts of data compression are shown:-
The Unary Code
The unary code of the non-negative integer n is defined as n-1 ones
followed by one zero or, alternatively, as n-1 zeros followed by a single one.
Table : Some Unary Codes
n
1
2
3
4
5
Code
0
10
110
1110
11110
Alt. Code
1
01
001
0001
00001
Entropy Coding
We can define the entropy of a signal symbol ai as –Pi log2Pi. This is
the smallest number of bits needed, on the average, to represent the symbol.
The amount of information contained in one, base-n symbol is:
n 1
H   Pi log 2 Pi
i 0
This quantity is called the entropy of the data being transited.
The entropy of the data depends on the individual probabilities Pi, and is
smallest when all n probabilities are equal.
Data Compression Strategies
There are different ways that data compression techniques can be
categorized, smith gives a compression classification as below:
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a. Lossless or Lossy
Lossless
Lossy
RLE
JPEG
Huffman
MPEG
Arithmetic
Vector quantization
Quadtree
b. Fixed or variable group size
Huffman
Group Size
Input
Fixed
Output
Variable
Arithmetic
Variable
Variable
RLE, LZW
Variable
Fixed
Method
Most data compression programs operate by taking a group of data from the
original file and compressed it in some way, and then writing the
compressed group to the output file.
1.1.2 Irreversible Text Compression
This method used to compress text by throwing away some
information .the decompressed text will not be identical to the original, so
such methods are not general purpose, they can be used in special cases.
Ex1//A run of consecutive blank spaces may be replaced by a single space.
Ex2// In extreme cases all text characters except letters and spaces may be
thrown away, and the letters may be case flattened (converted to all lower-
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or all uppercase). This will leave just 27 symbols, so a symbol can be
encoded in 5 instead of the usual 8 bits.
The compression ratio is 5/8 = .625, not bad, but the loss may normally be
too great.
Ad Hoc Text Compression
If the text contains many spaces but they are not clustered, they may be
removed and their positions indicated by a bit-string that contains a 0 for
each text character that is not a space and a 1 for each space. Thus, the text
Here are some ideas, is encoded as the bit-string “0000100010000100000”
followed by the text
Herearesomeideas.
If the number of blank spaces is small, the bit-string will be sparse.
Run-Length Encoding
The idea behind this approach to data compression is this: If a data item d
occurs n consecutive times in the input stream, replace the n occurrences
with the single pair nd. The n consecutive occurrences of a data item are
called a run length of n, and this approach to data compression is called run
length encoding or RLE. We apply this idea first to text compression then to
image compression.
a) RLE Text Compression
Just replacing “2._all_is_too_well” with “2._a2_is_t2_we2” will not
work. Clearly, the decompressor should have a way to tell that the first “2”
is part of the text while the others are repetition factors for the letters “o” and
“l”. Even the string “2._a2l_is t2o_we2l” does not solve this problem (and
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also does not provide any compression). One way to solve this problem is to
precede each repetition with a special escape character.
If we use the character “@” as the escape character, then the string
“2._a@2l_is_t@2o we@2l” can be decompressed unambiguously. However,
it is longer than the original string, since it replaces two consecutive letters
with three characters. We have to adopt the convention that only three or
more repetitions of the same character will be replaced with a repetition
factor. Figure 1.3a is a flowchart for such a simple run-length text
compressor.
After reading the first character, the count is 1 and the character is saved.
Subsequent characters are compared with the one already saved and, if they
are identical to it, the repeat-count is incremented. When a different
character is read, the operation depends on the value of the repeat count. If it
is small, the saved character is written on the compressed file and the newly
read character is saved. Otherwise, an “@” is written, followed by the
repeat-count and the saved character.
Decompression is also straightforward. It is shown in Figure 1.3b. When an
“@” is read, the repetition count n and the actual character are immediately
read, and the character is written n times on the output stream.
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