[CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example...
Transcript of [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example...
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Dictionary Techniques
C.M. LiuPerceptual Signal Processing Lab College of Computer ScienceNational Chiao-Tung University
Office: EC538(03)5731877
http://www.csie.nctu.edu.tw/~cmliu/Courses/Compression/
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Contents2
Overview
Introduction
Static Dictionary
Adaptive Dictionary
Applications
Summary
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Overview3
Statistical compression methods Use a statistical model of the data, and the quality of compression they achieve depends on how good that model is.
Dictionary-based compression methods Do not use a statistical model, nor do they use variable-size codes. The dictionary holds strings of symbols and it may be static or dynamic (adaptive). The former is permanent, sometimes allowing the addition of strings but no deletions, whereas the latter holds strings previously found in the input stream, allowing for additions and deletions of strings as new input is being read.
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Introduction4
So far we (largely) assumed symbol independenceNot true for many common data types
E.g., text, images, code
Basic ideaIdentify frequent symbol patterns.
Encode those more efficiently.
Use a default (less efficient) encoding for the rest.
Hope to come out ahead.
NotesThis looks reasonable for things like text.
Obviously won’t work for (close to) random data.
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Motivating Example5
Consider an ‘English’ source with26 letters & six punctuation marks.
Single-symbol, fixed-length encoding5 bits per symbol.
Four-symbol patterns, fixed-length encoding20 bits per symbol (324 = 220 = 1,048,576).
Assume uneven distributionpick a dictionary the 256 most-frequent patterns and encode them w/ 8bitsencode the rest with 20 bitsmust add 1-bit prefix to each to distinguish the two cases
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Motivating Example (2)6
If p is the probability of seeing a dictionary, then the bit rate is
R = 9p + 21(1-p) = 21 - 12p
Compression <=> 21 - 12p < 20=> p > 0.084
Not too badunder equal probability assumption, p = 0.00025
Bottom lineFor a specific application, we could devise an appropriate dictionary to maximize compression
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Digram Coding7
DictionaryAll letters from the alphabet +
As many digrams (pairs of letters) as possible
ExampleDictionary size = 256 entries
Alphabet: printable ASCII = 95
Digrams: 161 most common pairs
Another example: A = {a, b, c, d, r},
Dictionary:
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Digram Example8
Input: abracadabra
Output: 101
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Digram Example9
Input: --racadabra
Output: 101
X
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Digram Example10
Input: --racadabra
Output: 101100
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Digram Example11
Input: ---acadabra
Output: 101100110
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Digram Example12
Input: -----adadabra
Output: 101100110111
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Digram Example13
Input: -------abra
Output: 101100110111101
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Digram Example14
Input: ---------ra
Output: 101100110111101
X
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Digram Example15
Input: ---------ra
Output: 101100110111101100
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Digram Example16
Input: ----------a
Output: 101100110111101100000
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Problem: Which Digrams?17
Source #1: Textbook chapter (LaTeX) Source #2: C code
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Building Dictionaries Adaptively18
The beginningJacob Ziv/Abraham Lempel1977 (LZ77/LZ1), 1978 (LZ78/LZ2)1984 Terry Welch (LZW)
LZ77 vs. LZ78Two different approachesMultiple variationSource of several mainstream compression schemes
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LZ7719
General approachDictionary is a portion of the previously encoded sequence.sliding window compression
MechanismSearch buffer, look-ahead buffer, search pointerGoal:
find the maximum length match for the string pointed by the search pointer in the search bufferencode it
Rationaleif patterns tend to repeat locally, we should get more efficient representation
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LZ77 (2)20
(o)ffset = search ptr - match ptr = 7
(l)ength = number of consecutive letters matched = 4
(c)odeword(r)
Encoding<o, l, c> = <7, 4, C(‘r’)>
If |search buff| = S, |A| = A, S + |LA buff| = WFixed-length encoding: ⎡log2S⎤ + ⎡log2W⎤ + ⎡log2A⎤
Search pointer
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LZ77 Encoding Example21
SequencecabracadabrarrarradW = 13, S = 7
|cabraca|dabrar|rarradno match for dsend <0, 0, C(d)>|abracad|abrarr|arrad
|abracad|abrarr|arrad
|abracad|abrarr|arrad
|abracad|abrarr|arrad
Send <7, 4, C(r)>
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LZ77 Encoding Example(2)22
|cadabrar|rarrad|
|cadabrar|rarrad|
|cadabrar|rarrad|Send <3, 3, C(r)>
Could we do better?Send <3, 5, C(d)> instead!
Summary: three casesNo matchMatchMatch beyond the end of search buffer
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LZ77 Decoding Example 23
Input<0, 0, C(d)> <7, 4, C(r)> <3, 5, C(d)>
Outputcabraca
Decode: <0, 0, C(d)>Add a ‘d’: c|abracad|
Decode: <7, 4, C(r)>Start with the first ‘a’, copy four letters, decode C(r)cabrac|adabrar|
Decode: <3, 5, C(d)>Start with the first ‘r’, copy 3 letters:cabracada|brarrar|
copy 2 more letterscabracadabr|arrarar|
Decode C(d): cabracadabrarrarard
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LZ77 Variants24
So farAdaptive scheme, no prior knowledgeAsymptotically approaches case of full knowledge of source statisticsHowever, locality seems to play a non-trivial role
ImpovementsVariable-bit encoding
PKZip, Zip, Lharcm ONG, gzip, ARJVariable buffer size
Larger bugger requires faster searchesElimination of <0, 0, C(x)>
LZSS: simply use a flag bit
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LZ7825
LZ77 assumes locality of patterns
LZ78:No search buffer--explicit dictionary insteadEncoder/decoder must build dictionary in syncEncoding: <i, c>
i = index in dictionary tablec = code of following character
Example:wabba wabba wabba wabba woo woo woo
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LZ78 Example26
Index Entry
Dictionary:
Input: wabba wabba wabba wabba woo woo woo
Output:
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LZ78 Example (2)27
Dictionary:
Input: wabba wabba wabba wabba woo woo woo
Output:
<0, C(w)>
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LZ78 Example (3)28
Index Entry
1 w
2 a
Dictionary:
Input: -abba wabba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
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LZ78 Example (4)29
Index Entry
1 w
2 a
3 b
Dictionary:
Input: --bba wabba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
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LZ78 Example (5)30
Index Entry
1 w
2 a
3 b
4 ba
Dictionary:
Input: ---ba wabba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
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LZ78 Example (6)31
Index Entry
1 w
2 a
3 b
4 ba
5
Dictionary:
Input: ----- wabba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
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LZ78 Example (7)32
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
Dictionary:
Input: ------wabba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
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LZ78 Example (8)33
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
Dictionary:
Input: --------bba wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
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LZ78 Example (9)34
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
Dictionary:
Input: ----------a wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
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LZ78 Example (10)35
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
Dictionary:
Input: ------------wabba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
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LZ78 Example (11)36
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
Dictionary:
Input: ---------------ba wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
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LZ78 Example (12)37
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
Dictionary:
Input: ------------------wabba woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
11 wabb
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LZ78 Example (13)38
Dictionary:
Input: ----------------------a woo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
11 wabb
12 a w
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
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LZ78 Example (14)39
Dictionary:
Input: -------------------------oo woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
<0, C(o)>
11 wabb
12 a w
13 o
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
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LZ78 Example (15)40
Dictionary:
Input: --------------------------o woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
<0, C(o)>
<13, C( )>
11 wabb
12 a w
13 o
14 o
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
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LZ78 Example (16)41
Dictionary:
Input: ----------------------------woo woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
<0, C(o)>
<13, C( )>
<1, C(o)>
11 wabb
12 a w
13 o
14 o
15 wo
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
![Page 42: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/42.jpg)
LZ78 Example (17)42
Dictionary:
Input: ------------------------------o woo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
<0, C(o)>
<13, C( )>
<1, C(o)>
<14, C(w)>
11 wabb
12 a w
13 o
14 o
15 wo
16 o w
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
![Page 43: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/43.jpg)
LZ78 Example (18)43
Dictionary:
Input: ---------------------------------oo
Output:
<0, C(w)>
<0, C(a)>
<0, C(b)>
<3, C(a)>
<0, C( )>
<1, C(a)>
<3, C(b)>
<2, C( )>
<6, C(b)>
<4, C( )>
<9, C(b)>
<8, C(w)>
<0, C(o)>
<13, C( )>
<1, C(o)>
<14, C(w)>
<13, C(o)>
11 wabb
12 a w
13 o
14 o
15 wo
16 o w
17 oo
Index Entry
1 w
2 a
3 b
4 ba
5
6 wa
7 bb
8 a
9 wab
10 ba
![Page 44: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/44.jpg)
LZ78 Notes44
ObservationIf we keep on encoding the dictionary will keep on growing
Practical choicesStop growing the dictionary
effectively switch to a static dictionaryPrune it
e.g. based on usage statisticsReset it
Start all over againWithout specific knowledge of the source, neither of these may work well!
![Page 45: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/45.jpg)
LZ78 Variants: LZW45
Terry Welch (1984)Idea
Instead of <i, c>, encode i only
AlgorithmSeed dictionary with all alphabet letters, p = nullwhile( !done)a = get_next_symbolif( p · a) is in dictionary
p = p · a
elsesend out index of pp = a
endwhile
![Page 46: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/46.jpg)
LZW Encoding46
Index Entry
1
2 a
3 b
4 o
5 w
6
7
8
9
10
Dictionary: Output:
Input: wabba wabba wabba wabba woo woo woo
p =
![Page 47: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/47.jpg)
LZW Encoding (2)47
Index Entry
1
2 a
3 b
4 o
5 w
6
7
8
9
10
Dictionary: Output:
Input: wabba wabba wabba wabba woo woo woo
p = w
![Page 48: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/48.jpg)
LZW Encoding (3)48
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7
8
9
10
Dictionary: Output:
5 (‘w’)
Input: -abba wabba wabba wabba woo woo woo
p = wa
![Page 49: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/49.jpg)
LZW Encoding (4)49
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8
9
10
Dictionary: Output:
5 (‘w’)
2 (‘a’)
Input: --bba wabba wabba wabba woo woo woo
p = ab
![Page 50: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/50.jpg)
LZW Encoding (5)50
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9
10
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
Input: ---ba wabba wabba wabba woo woo woo
p = bb
![Page 51: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/51.jpg)
LZW Encoding (6)51
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
Input: ----a wabba wabba wabba woo woo woo
p = ba
![Page 52: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/52.jpg)
LZW Encoding (7)52
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
Input: ----- wabba wabba wabba woo woo woo
p = a
![Page 53: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/53.jpg)
LZW Encoding (8)53
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
Input: ------wabba wabba wabba woo woo woo
Index Entry
11 w
12
13
14
15
16
17
18
19
20
p = w
![Page 54: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/54.jpg)
LZW Encoding (9)54
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
Input: -------abba wabba wabba woo woo woo
Index Entry
11 w
12
13
14
15
16
17
18
19
20
p = wa
![Page 55: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/55.jpg)
LZW Encoding (10)55
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
Input: --------bba wabba wabba woo woo woo
Index Entry
11 w
12 wab
13
14
15
16
17
18
19
20
p = wab
![Page 56: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/56.jpg)
LZW Encoding (11)56
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
Input: ---------ba wabba wabba woo woo woo
Index Entry
11 w
12 wab
13
14
15
16
17
18
19
20
p = bb
![Page 57: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/57.jpg)
LZW Encoding (12)57
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
Input: ----------a wabba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14
15
16
17
18
19
20
p = bba
![Page 58: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/58.jpg)
LZW Encoding (13)58
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
Input: ----------- wabba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14
15
16
17
18
19
20
p = a
![Page 59: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/59.jpg)
LZW Encoding (14)59
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
Input: ------------wabba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
p = a w
![Page 60: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/60.jpg)
LZW Encoding (15)60
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
Input: -------------abba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
p = wa
![Page 61: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/61.jpg)
LZW Encoding (16)61
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
Input: --------------bba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
p = wab
![Page 62: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/62.jpg)
LZW Encoding (17)62
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
Input: ---------------ba wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16
17
18
19
20
p = wabb
![Page 63: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/63.jpg)
LZW Encoding (18)63
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
Input: ----------------a wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16
17
18
19
20
p = ba
![Page 64: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/64.jpg)
LZW Encoding (19)64
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
Input: ----------------- wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17
18
19
20
p = ba
![Page 65: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/65.jpg)
LZW Encoding (20)65
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
Input: ------------------wabba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17
18
19
20
p = w
![Page 66: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/66.jpg)
LZW Encoding (21)66
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
Input: -------------------abba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18
19
20
p = wa
![Page 67: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/67.jpg)
LZW Encoding (22)67
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
Input: --------------------bba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18
19
20
p = ab
![Page 68: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/68.jpg)
LZW Encoding (23)68
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
Input: ---------------------ba woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19
20
p = abb
![Page 69: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/69.jpg)
LZW Encoding (24)69
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
Input: ----------------------a woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19
20
p = ba
![Page 70: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/70.jpg)
LZW Encoding (25)70
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
Input: ----------------------- woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19
20
p = ba
![Page 71: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/71.jpg)
LZW Encoding (26)71
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ------------------------woo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20
p = ba w
![Page 72: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/72.jpg)
LZW Encoding (27)72
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: -------------------------oo woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = wo
5 (‘w’)
![Page 73: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/73.jpg)
LZW Encoding (28)73
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: --------------------------o woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = oo
5 (‘w’)
4 (‘o’)
Index Entry
21 oo
22
23
24
25
26
27
28
29
30
![Page 74: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/74.jpg)
LZW Encoding (29)74
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: --------------------------- woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = o
5 (‘w’)
4 (‘o’)
4 (‘o’)
Index Entry
21 oo
22 o
23
24
25
26
27
28
29
30
![Page 75: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/75.jpg)
LZW Encoding (30)75
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ----------------------------woo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = w
5 (‘w’)
4 (‘o’)
4 (‘o’)
Index Entry
21 oo
22 o
23
24
25
26
27
28
29
30
![Page 76: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/76.jpg)
LZW Encoding (31)76
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: -----------------------------oo woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = wo
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
Index Entry
21 oo
22 o
23 wo
24
25
26
27
28
29
30
![Page 77: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/77.jpg)
LZW Encoding (32)77
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ------------------------------o woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = oo
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
Index Entry
21 oo
22 o
23 wo
24
25
26
27
28
29
30
![Page 78: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/78.jpg)
LZW Encoding (33)78
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ------------------------------- woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = oo
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
21 (‘oo’)
Index Entry
21 oo
22 o
23 wo
24 oo
25
26
27
28
29
30
![Page 79: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/79.jpg)
LZW Encoding (34)79
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: --------------------------------woo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = w
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
21 (‘oo’)
Index Entry
21 oo
22 o
23 wo
24 oo
25
26
27
28
29
30
![Page 80: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/80.jpg)
LZW Encoding (35)80
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ---------------------------------oo
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = wo
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
21 (‘oo’)
Index Entry
21 oo
22 o
23 wo
24 oo
25
26
27
28
29
30
![Page 81: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/81.jpg)
LZW Encoding (36)81
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: ----------------------------------o
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = woo
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
21 (‘oo’)
23 (‘ wo’)
Index Entry
21 oo
22 o
23 wo
24 oo
25 wo
o
26
27
28
29
30
![Page 82: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/82.jpg)
LZW Encoding (EOT)82
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary: Output:
5 (‘w’)
2 (‘a’)
3 (‘b’)
3 (‘b’)
2 (‘a’)
1 (‘ ’)
6 (‘wa’)
8 (‘bb’)
10 (‘a ’)
12 (‘wab’)
9 (‘ba’)
11 (‘ w’)
7 (‘ab’)
16 (‘ba ’)
Input: -----------------------------------
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17 wa
18 abb
19 ba w
20 wo
p = o
5 (‘w’)
4 (‘o’)
4 (‘o’)
11 (‘ w’)
21 (‘oo’)
23 (‘ wo’)
4 (‘o’)
Index Entry
21 oo
22 o
23 wo
24 oo
25 wo
o
26
27
28
29
30
![Page 83: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/83.jpg)
LZW Decoding83
Index Entry
1
2 a
3 b
4 o
5 w
6
7
8
9
10
Dictionary:
Input: 5 2 3 3 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p =
Output:
![Page 84: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/84.jpg)
LZW Decoding (2)84
Index Entry
1
2 a
3 b
4 o
5 w
6
7
8
9
10
Dictionary:
Input: 5 2 3 3 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = w
Output: w
![Page 85: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/85.jpg)
LZW Decoding (3)85
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7
8
9
10
Dictionary:
Input: - 2 3 3 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = wa
Output: wa
![Page 86: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/86.jpg)
LZW Decoding (4)86
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8
9
10
Dictionary:
Input: - - 3 3 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = ab
Output: wab
![Page 87: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/87.jpg)
LZW Decoding (5)87
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9
10
Dictionary:
Input: - - - 3 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = bb
Output: wabb
![Page 88: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/88.jpg)
LZW Decoding (6)88
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10
Dictionary:
Input: - - - - 2 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = ba
Output: wabba
![Page 89: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/89.jpg)
LZW Decoding (7)89
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - 1 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = a
Output: wabba
![Page 90: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/90.jpg)
LZW Decoding (8)90
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - 6 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = wa
Output: wabba wa
Index Entry
11 w
12
13
14
15
16
17
18
19
20
![Page 91: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/91.jpg)
LZW Decoding (9)91
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = wa
Output: wabba wa
Index Entry
11 w
12
13
14
15
16
17
18
19
20
![Page 92: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/92.jpg)
LZW Decoding (10)92
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - 8 10 12 9 11 7 16 5 4 4 11 21 23 4
p = wabb
Output: wabba wabb
Index Entry
11 w
12 wab
13
14
15
16
17
18
19
20
![Page 93: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/93.jpg)
LZW Decoding (11)93
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - 10 12 9 11 7 16 5 4 4 11 21 23 4
p = bb
Output: wabba wabb
Index Entry
11 w
12 wab
13
14
15
16
17
18
19
20
![Page 94: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/94.jpg)
LZW Decoding (12)94
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - 10 12 9 11 7 16 5 4 4 11 21 23 4
p = bba
Output: wabba wabba
Index Entry
11 w
12 wab
13 bba
14
15
16
17
18
19
20
![Page 95: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/95.jpg)
LZW Decoding (13)95
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - 12 9 11 7 16 5 4 4 11 21 23 4
p = bba
Output: wabba wabba
Index Entry
11 w
12 wab
13 bba
14
15
16
17
18
19
20
![Page 96: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/96.jpg)
LZW Decoding (14)96
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - 12 9 11 7 16 5 4 4 11 21 23 4
p = a
Output: wabba wabba
Index Entry
11 w
12 wab
13 bba
14
15
16
17
18
19
20
![Page 97: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/97.jpg)
LZW Decoding (15)97
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - 12 9 11 7 16 5 4 4 11 21 23 4
p = a wab
Output: wabba wabba wab
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
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LZW Decoding (16)98
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - 9 11 7 16 5 4 4 11 21 23 4
p = wab
Output: wabba wabba wab
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
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LZW Decoding (16)99
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - 9 11 7 16 5 4 4 11 21 23 4
p = wab
Output: wabba wabba wab
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
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LZW Decoding (17)100
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - 9 11 7 16 5 4 4 11 21 23 4
p = wab
Output: wabba wabba wab
Index Entry
11 w
12 wab
13 bba
14 a w
15
16
17
18
19
20
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LZW Decoding (18)101
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - 9 11 7 16 5 4 4 11 21 23 4
p = wabba
Output: wabba wabba wabba
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16
17
18
19
20
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LZW Decoding (19)102
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - - 11 7 16 5 4 4 11 21 23 4
p = ba
Output: wabba wabba wabba
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16
17
18
19
20
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LZW Decoding (20)103
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - - 11 7 16 5 4 4 11 21 23 4
p = ba w
Output: wabba wabba wabba w
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17
18
19
20
![Page 104: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/104.jpg)
LZW Decoding (21)104
Index Entry
1
2 a
3 b
4 o
5 w
6 wa
7 ab
8 bb
9 ba
10 a
Dictionary:
Input: - - - - - - - - - - - - 7 16 5 4 4 11 21 23 4
p = w
Output: wabba wabba wabba w
Index Entry
11 w
12 wab
13 bba
14 a w
15 wabb
16 ba
17
18
19
20
… and so on …
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LZW Special Case105
The presented decoder issimple, elegant, and … wrongbut fixable
Example:A = {a, b}
Input: abababab …
Starting dictionaryIndex Entry
1 a
2 b
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LZW Special Case: Encoding106
Index Entry
1 a
2 b
Dictionary: Output:
Input: abababababab …
p =
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LZW Special Case: Encoding (2)107
Index Entry
1 a
2 b
Dictionary: Output:
Input: abababababab …
p = a
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LZW Special Case: Encoding (3)108
Index Entry
1 a
2 b
3 ab
Dictionary: Output:
1 (‘a’)
Input: -bababababab …
p = ab
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LZW Special Case: Encoding (4)109
Index Entry
1 a
2 b
3 ab
4 ba
Dictionary: Output:
1 (‘a’)
2 (‘b’)
Input: --ababababab …
p = ba
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LZW Special Case: Encoding (5)110
Index Entry
1 a
2 b
3 ab
4 ba
Dictionary: Output:
1 (‘a’)
2 (‘b’)
Input: ---babababab …
p = ab
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LZW Special Case: Encoding (6)111
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary: Output:
1 (‘a’)
2 (‘b’)
3 (‘ab’)
Input: ----abababab …
p = aba
![Page 112: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/112.jpg)
LZW Special Case: Encoding (7)112
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary: Output:
1 (‘a’)
2 (‘b’)
3 (‘ab’)
Input: -----bababab …
p = ab
![Page 113: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/113.jpg)
LZW Special Case: Encoding (8)113
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary: Output:
1 (‘a’)
2 (‘b’)
3 (‘ab’)
Input: ------ababab …
p = aba
![Page 114: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/114.jpg)
LZW Special Case: Encoding (9)114
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
6 abab
Dictionary: Output:
1 (‘a’)
2 (‘b’)
3 (‘ab’)
5 (‘aba’)
Input: -------babab …
p = abab
![Page 115: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/115.jpg)
LZW Special Case: Decoding115
Index Entry
1 a
2 b
Dictionary:
Input: 1 2 3 5 …
p =
Output:
We need to know in advance the initial dictionary used, but we can reconstruct the additional entries as we go, since they are always simply concatenations of previous entries.
the newly-created dictionary word is sent immediately
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LZW Special Case: Decoding (2)116
Index Entry
1 a
2 b
Dictionary:
Input: 1 2 3 5 …
p = a
Output: a
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LZW Special Case: Decoding (3)117
Index Entry
1 a
2 b
3 ab
Dictionary:
Input: - 2 3 5 …
p = ab
Output: ab
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LZW Special Case: Decoding (4)118
Index Entry
1 a
2 b
3 ab
4 ba
Dictionary:
Input: - - 3 5 …
p = bab
Output: abab
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LZW Special Case: Decoding (5)119
Index Entry
1 a
2 b
3 ab
4 ba
Dictionary:
Input: - - - 5 …
p = ab
Output: abab
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LZW Special Case: Decoding (6)120
Index Entry
1 a
2 b
3 ab
4 ba
Dictionary:
Input: - - - 5 …
p = ab???
Output: abab???
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LZW Special Case: Decoding (7)121
We know that 5th entry will start with ‘ab’
We can add it to p and continue decoding
Index Entry
1 a
2 b
3 ab
4 ba
5 ab…
Dictionary:
Input: - - - 5 …
p = ab???
Output: abab???
![Page 122: [CSCI 6990-DC] 05: Dictionary Techniquescmliu/Courses/Compression/chap5.pdf · Motivating Example (2) 6 If p is the probability of seeing a dictionary, then the bit rate is R = 9](https://reader036.fdocuments.net/reader036/viewer/2022071501/6120f32fdd980c25b8477149/html5/thumbnails/122.jpg)
LZW Special Case: Decoding (8)122
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary:
Input: - - - 5 …
p = abab?
Output: abab???
But, since it was sent immediately, it must also start with "whatever comes next", and so must end with the same symbol it starts with, namely a.
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LZW Special Case: Decoding (9)123
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary:
Input: - - - 5 …
p = ababa
Output: abab???
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LZW Special Case: Decoding (10)124
Index Entry
1 a
2 b
3 ab
4 ba
5 aba
Dictionary:
Input: - - - - …
p = aba
Output: abababa
Decoder must have an exception handler for such cases.General case, cScSc, where c is a single character, S is
a string
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LZW Patents (http://en.wikipedia.org/wiki/Lempel-Ziv-Welch)
125
Various patents have been issued in the United States and other countries for LZW and similar algorithms. LZ78 was covered by U.S. Patent 4,464,650 by Lempel, Ziv, Cohn, and Eastman, assigned to Sperry Corporation, later Unisys Corporation, filed on August 10, 1981. Two US patents were issued for the LZW algorithm: U.S. Patent 4,814,746 by Victor S. Miller and Mark N. Wegman and assigned to IBM, originally filed on June 1, 1983, and U.S. Patent 4,558,302 by Welch, assigned to Sperry Corporation, later Unisys Corporation, filed on June 20, 1983. On June 20, 2003, this patent on the LZW algorithm expired [1].US Patent 4,558,302 received a lot of negative press after LZW compression was used in the GIF image format (see Graphics Interchange Format#Unisys and LZW patent enforcement).
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Applications: compress126
An early implementation of LZWAdaptive dictionaryStart with 512 entries (9-bit codewords)When it fills up— doubles dictionary size (codewordsbecome longer by a bit)Max codeword length bmax = 9..16When dictionary reaches 2bmax entries
it becomes a static dictionary encoderIf compression ration falls below a threshold, dictionary is reset
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Applications: GIF127
LZW scheme, similar to compress:Clear code: b bits/pixel 2b clear codesStarting dictionary 2b+1
Dictionary size doubles as in compressMax size = 4096 entries, static dictionaryFormat:
Codewords stored in blocks of characters up to 255Each block has a header with countBlock terminator: 8 zero bitsEnd of image info: 2b+1 (before block terminator)
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GIF Performance128
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Applications: PNG129
Patent-free alternative to GIF (libpng.org)Designed specifically for lossless image compressionModes
True color, grayscale, 8-bit palletteTwo autonomous compression componentsdeflate (RFC 1951)—LZ77-style dictionary compression algorithm + Huffmanfiltering—lossless transformations of byte-level image data
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Deflate130
Deflate = LZ77 + Huffman
Three types of (zlib) data blocksUncompressed, LZ77 + fixed Huffman, LZ77 + dynamic Huffman
Match is b/w 3 & 258 bytesA sliding window of 3 bytes is examinedIf match is not found, encode first byte and slide window`
LZ77 outputliteral<match_length, offset>
Combined alphabet = literals + match_lengthsCodes 0-255 == literals256 = end-of-block257-285: rangefollowed by selector bits
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Deflate Match Length Codes131
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Huffman Codes for Match Lengths132
Note: offset (1..32768) is coded with a different Huffman code!
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Match Length Code133
0–3: distances 1–4 4–5: distances 5–8, 1 extra bit 6–7: distances 9–16, 2 extra bits 8–9: distances 17–32, 3 extra bits ... 26–27: distances 8193–16384, 12 extra bits 28–29: distances 16385–32768, 13 extra bits 30–31: not used, reserved and illegal but still part of the tree.
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PNG: Compression Filters134
Image layoutScanlines: left-to-right, top-to-bottom
Filters are applied on a scanline-by-scanline basisAll algorithms applied to bytes (not pixels!)Filter types
None Unmodified value
SubDifference from previous value (mod 256)
UpLike Sub, except the previous pixel is above
AverageSubtract average( left, above)
PaethDifference with nearest(left, above, upper_left)
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PNG: Performance135
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Summary136
Introduced dictionary techniquesTend to work well for text & communication protocolsStatic techniques are suitable for known data domain
Adaptive techniques LZ77LZ78LZW
Combination with HuffmanDeflate
Practical applicationsGIF, zlip --> png, pdf, …
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Homeworks137
Homeworks (Sayood 3rd, pp.139-140)Deadline April 23, 4, 5, 6, 7, 8