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Technical Seminar Presentation 2005
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A Review of Data Compression Techniques
Presented by
Sudeepta Mishra Roll# CS200117052
At
NIST,Berhampur
Under the guidance of Mr. Rowdra Ghatak
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Introduction
• Data compression is the process of encoding data so that it takes less storage space or less transmission time than it would if it were not compressed.
• Compression is possible because most real-world data is very redundant
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Different Compression Techniques
• Mainly two types of data Compression techniques are there.
– Loss less Compression.
Useful in spreadsheets, text, executable program Compression.
– Lossy less Compression.
Compression of images, movies and sounds.
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Types of Loss less data Compression
• Dictionary coders.
– Zip (file format).
– Lempel Ziv.
• Entropy encoding.
– Huffman coding (simple entropy coding).
• Run-length encoding.
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Dictionary-Based Compression
• Dictionary-based algorithms do not encode single symbols as variable-length bit strings; they encode variable-length strings of symbols as single tokens.
• The tokens form an index into a phrase dictionary.
• If the tokens are smaller than the phrases they replace, compression occurs.
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Types of Dictionary
• Static Dictionary.
• Semi-Adaptive Dictionary.
• Adaptive Dictionary.
– Lempel Ziv algorithms belong to this category of dictionary coders. The dictionary is being built in a single pass, while at the same time encoding the data.
– The decoder can build up the dictionary in the same way as the encoder while decompressing the data.
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• Using a English Dictionary the string:
“A good example of how dictionary based compression works”
• Gives : 1/1 822/3 674/4 1343/60 928/75 550/32 173/46 421/2
• Using the dictionary as lookup table, each word is coded as x/y, where, x gives the page no. and y gives the number of the word on that page. If the dictionary has 2,200 pages with less than 256 entries per page: Therefore x requires 12 bits and y requires 8 bits, i.e., 20 bits per word (2.5 bytes per word). Using ASCII coding the above string requires 48 bytes, whereas our encoding requires only 20 (<-2.5 * 8) bytes: 50% compression.
Dictionary-Based Compression: Example
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Lempel Ziv
• It is a family of algorithms, stemming from the two algorithms proposed by Jacob Ziv and Abraham Lempel in their landmark papers in 1977 and 1978.
LZ77 LZ78
LZR
LZHLZSS LZB
LZFG
LZC LZT LZMW
LZW
LZJ
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LZW Algorithm
• It is An improved version of LZ78 algorithm.
• Published by Terry Welch in 1984.
• A dictionary that is indexed by “codes” is used. The dictionary is assumed to be initialized with 256 entries (indexed with ASCII codes 0 through 255) representing the ASCII table.
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The LZW Algorithm (Compression)
W = NIL;while (there is input){K = next symbol from input;if (WK exists in the dictionary) {W = WK;} else {output (index(W));add WK to the dictionary;W = K;}}
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The LZW Algorithm (Compression) Flow Chart
START
W= NULL
IS EOF?
K=NEXT INPUT
IS WKFOUND?W=WK
OUTPUT INDEX OF W
ADD WK TO DICTIONARY
STOP
W=K
YES
NO
YES
NO
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The LZW Algorithm (Compression) Example
• Input string is • The Initial
Dictionarycontains symbols like a, b, c, d with their index values as 1, 2, 3, 4 respectively.
• Now the input string is read from left to right. Starting from a.
a b d c a d a c
a 1
b 2
c 3
d 4
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• W = Null
• K = a
• WK = a
In the dictionary.
a b d c a d a c
a 1
b 2
c 3
d 4
K
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = b.
• WK = ab
is not in the dictionary.
• Add WK to dictionary
• Output code for a.
• Set W = b
a b d c a d a c
K
1
ab 5a 1
b 2
c 3
d 4
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = d
• WK = bd
Not in the dictionary.
Add bd to dictionary.
• Output code b
• Set W = d
a b d c a d a c
1
K
2
ab 5a 1
b 2
c 3
d 4
bd 6
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = a
• WK = da
not in the dictionary.
• Add it to dictionary.
• Output code d
• Set W = a
a b d a b d a c
1
K
2 4
ab 5a 1
b 2
c 3
d 4
bd 6
da 7
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = b
• WK = ab
It is in the dictionary.
a b d a b d a c
1
K
2 4
ab 5a 1
b 2
c 3
d 4
bd 6
da 7
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = d
• WK = abd
Not in the dictionary.
• Add W to the dictionary.
• Output code for W.
• Set W = d
a b d a b d a c
1
K
2 4 5
ab 5a 1
b 2
c 3
d 4
bd 6
da 7
abd 8
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = a
• WK = da
In the dictionary.
a b d a b d a c
1
K
2 4 5
ab 5a 1
b 2
c 3
d 4
bd 6
da 7
abd 8
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• K = c
• WK = dac
Not in the dictionary.
• Add WK to the dictionary.
• Output code for W.
• Set W = c
• No input left so output code for W.
a b d a b d a c
1
K
2 4 5
ab 5a 1
b 2
c 3
d 4
bd 6
da 7
abd 8
7
dac 9
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Sudeepta Mishra CS200117052
The LZW Algorithm (Compression) Example
• The final output string is
1 2 4 5 7 3
• Stop.
cadbadba
1
K
2 4 5
5ab
4d
3c
2b
1a
6bd
7da
8abd
7
9dac
3
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LZW Decompression Algorithm
read a character k;
output k;
w = k;
while ( read a character k )
/* k could be a character or a code. */
{ entry = dictionary entry for k;
output entry;
add w + entry[0] to dictionary;
w = entry; }
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LZW Decompression Algorithm Flow Chart
START
Output K
IS EOF?
K=NEXT INPUT
ENTRY=DICTIONARY INDEX (K)
ADD W+ENTRY[0] TO DICTIONARY
STOP
W=ENTRY
K=INPUT
W=K
YES
NO
Output ENTRY
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 1
• Out put K (i.e. a)
• W = K
1
K
2 4 5
4d
3c
2b
1a
7 3
a
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 2
• entry = b
• Output entry
• Add W + entry[0] to dictionary
• W = entry[0] (i.e. b)
1
K
2 4 5
4d
3c
2b
1a
7 3
a b
5ab
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 4
• entry = d
• Output entry
• Add W + entry[0] to dictionary
• W = entry[0] (i.e. d)
1
K
2 4 5
4d
3c
2b
1a
7 3
a b
5ab
6bd
d
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 5
• entry = ab
• Output entry
• Add W + entry[0] to dictionary
• W = entry[0] (i.e. a)
1
K
2 4 5
4d
3c
2b
1a
7 3
a b
5ab
6bd
d a b
7da
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 7
• entry = da
• Output entry
• Add W + entry[0] to dictionary
• W = entry[0] (i.e. d)
1
K
2 4 5
4d
3c
2b
1a
7 3
a b
5ab
6bd
d a b
7da
d a
8abd
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Sudeepta Mishra CS200117052
The LZW Algorithm (Decompression) Example
• K = 3
• entry = c
• Output entry
• Add W + entry[0] to dictionary
• W = entry[0] (i.e. c)
1
K
2 4 5
4d
3c
2b
1a
7 3
a b
5ab
6bd
d a b
7da
d a
8abd
c
9dac
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Sudeepta Mishra CS200117052
Advantages
• As LZW is adaptive dictionary coding no need to transfer the dictionary explicitly.
• It will be created at the decoder side.
• LZW can be made really fast, it grabs a fixed number of bits from input, so bit parsing is very easy, and table look up is automatic.
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Problems with the encoder
• What if we run out of space?
– Keep track of unused entries and use LRU (Last Recently Used).
– Monitor compression performance and flush dictionary when performance is poor.
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Sudeepta Mishra CS200117052
Conclusion
• LZW has given new dimensions for the development of new compression techniques.
• It has been implemented in well known compression format like Acrobat PDF and many other types of compression packages.
• In combination with other compression techniques many other different compression techniques are developed like LZMS.
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REFERENCES
[1] http://www.bambooweb.com/articles/d/a/Data_Compression.html[2] http://tuxtina.de/files/seminar/LempelZivReport.pdf[3] BELL, T. C., CLEARY, J. G., AND WITTEN, I. H. Text
Compression. Prentice Hall, Upper Sadle River, NJ, 1990.[4] http://www.cs.cf.ac.uk/Dave/Multimedia/node214.html[5] http://download.cdsoft.co.uk/tutorials/rlecompression/Run-
Length Encoding (RLE) Tutorial.htm[6] David Salomon, Data Compression The Complete Reference,
Second Edition. Springer-Verlac, New York, Inc, 2001 reprint.[7] http://www.programmersheaven.com/2/Art_Huffman_p1.htm[8] http://www.programmersheaven.com/2/Art_Huffman_p2.htm[9] Khalid Sayood, Introduction to Data Compression Second
Edition, Chapter 5, pp. 137-157, Harcourt India Private Limited.
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Thank You
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