Two-dimensional information theory and coding: with application to graphics and high-density storage media
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2010
|
Ausgabe: | 1. publ. |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | Includes bibliographical references and index |
Beschreibung: | IX, 171 S. |
ISBN: | 9780521888608 |
Internformat
MARC
LEADER | 00000nam a2200000zc 4500 | ||
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245 | 1 | 0 | |a Two-dimensional information theory and coding |b with application to graphics and high-density storage media |c Jørn Justesen and Søren Forchhammer |
250 | |a 1. publ. | ||
264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2010 | |
300 | |a IX, 171 S. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
500 | |a Includes bibliographical references and index | ||
650 | 4 | |a Mathematik | |
650 | 4 | |a Mathematisches Modell | |
650 | 4 | |a Coding theory | |
650 | 4 | |a Information storage and retrieval systems |x Mathematics | |
650 | 4 | |a Bipartite graphs | |
650 | 4 | |a Computer storage devices |x Mathematical models | |
650 | 4 | |a Computer graphics |x Mathematics | |
650 | 4 | |a Data visualization | |
650 | 4 | |a Binary system (Mathematics) | |
650 | 0 | 7 | |a Speichermedien |0 (DE-588)4351464-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
_version_ | 1804140755422281728 |
---|---|
adam_text | Contents
Preface
page
χί
Introduction to information theory
1
1.1
Introduction
1
1.2
Entropy of discrete sources
1
1.3
Mutual information and discrete memoryless channels
4
1.4
Source coding for discrete sources
5
1.4.1
The Kraft inequality
6
1.4.2
Huffman coding
7
1.5
Arithmetic codes
8
1.5.1
Ideal arithmetic coding
9
1.5.2
Finite-precision arithmetic coding
10
1.5.3
Decoding arithmetic codes
11
1.5.4
Universal codes
12
1.6
Entropy of images
13
1.7
Notes
14
Exercises
15
References
16
Finite-state sources
17
2.1
Introduction
17
2.2
Finite-state sources
17
2.2.1
Constrained sequences
18
2.2.2
Counting constrained sequences
18
2.3
Markov sources and Markov chains
19
2.3.1
Stationary distribution
20
2.3.2
Reversal of a Markov chain
20
2.3.3
Markov sources
20
2.4
Entropy of Markov chains and Markov sources
21
2.4.1
Stochastic processes
21
2.4.2
Entropy of Markov chains and Markov sources
21
2.5
Maximum-entropy Markov chains
22
2.6
Source coding for Markov chains
24
2.7
Elementary two-dimensional sources
24
Contents
2.7.1
Structure
in
two-dimensional
sources
24
2.7.2
Bands of finite height
26
2.7.3
Causal models
26
2.8
Pickard random fields
28
2.8.1
Independence assumptions
28
2.8.2
Probability on a rectangle
29
2.8.3
Constructing a two-dimensional random field from a
Markov chain
29
2.8.4
Symmetric Pickard random fields
32
2.9
Markov random fields
33
2.10
Notes
34
Exercises
34
References
35
Channels and linear codes
36
3.1
Introduction
36
3.2
Channel capacity and codes
36
3.2.1
Discrete memoryless channels and capacity
36
3.2.2
Codes for discrete memoryless channels
38
3.3
Linear codes
39
3.3.1
Linear codes and vector spaces
39
3.3.2
Decodable errors
40
3.3.3
Hamming codes and their duals
42
3.3.4
Cyclic codes and generator polynomials
43
3.3.5
Orthogonal sequences and arrays for synchronization
44
3.3.6
Product codes
45
3.4
Error probability and error exponents
46
3.4.1
The union bound for block codes
46
3.4.2
A bound for rates close to capacity
47
3.4.3
Performance of specific codes on the
BSC 49
3.5
Other applications of linear codes in information theory
50
3.5.1
Rate-distortion functions
50
3.5.2
Encoding of correlated sources
51
3.6
Notes
52
Exercises
52
References
53
Reed-Solomon codes and their decoding
54
4.1
Introduction
54
4.2
Finite fields
54
4.3
Definition of Reed-Solomon codes
55
4.4
Decoding by interpolation
56
4.5
Decoding from syndromes
58
4.6
Reed-Solomon codes over the fields
Fil 1
) 61
Contents
4.7
Faster decoding methods
62
4.8
Reed-Solomon codes and
q
-ary
channels
64
4.9
Notes
65
Exercises
65
Source coding
66
5.1
Context-based adaptive coding of sources with memory
67
5.1.1
Two-part coding
68
5.1.2
Context-adaptive code length
68
5.1.3
Context-based adaptive image coding
70
5.1.4
Context-based coding of binary images
71
5.2
Universal coding
72
5.2.1
Lempel-Ziv coding
73
5.2.2
Algorithm Context
76
5.3
Dynamic context algorithms
80
5.4
Code lengths and estimation of entropy
82
5.5
Notes
83
Exercises
84
References
85
Information in two-dimensional media
86
6.1
Introduction
86
6.2
Images and documents such as two-dimensional media
86
6.2.1
Mixed media and document layout
87
6.2.2
Compound documents
88
6.3
Media components
88
6.3.1
Printed text
89
6.3.2
Maps and line drawings
89
6.3.3
Natural images
93
6.4
Context-based coding of two-dimensional media
96
6.4.1
Lossless context-based coding
97
6.4.2
Context quantization
98
6.4.3
Lossy context-based coding
101
6.5
Context-based multiple representations
103
6.5.1
Refinement coding for quality progression
103
6.5.2
Multi-resolution context-based coding
104
6.5.3
Context-based coding of maps and layered graphics
105
6.6
Model-based coding of two-dimensional document components
107
6.6.1
Symbol-based coding of text
108
6.6.2
Coding of halftone images
109
6.7
Image coding
110
6.7.1
Predictive image coding
110
6.7.2
Transform-based image coding
113
6.7.3
Subband- and wavelet-based image coding
114
vi ¡i
Contents
6.8
Coding of
compound
documents
116
6.8.1
Coding
document segments
116
6.8.2
Coding mixed raster
content
117
6.9
Notes
117
Exercises
118
References
118
Constrained two-dimensional fields for storage
119
7.1
Introduction
119
7.2
Two-dimensional fields with a finite constraint
119
7.3
Counting two-dimensional patterns with constraints
121
7.4
Bands of finite height
123
7.4.1
Bounds for first-order-symmetric constraints
124
7.4.2
Markov chains on bands
126
7.5
Causal models in two dimensions
127
7.5.1
Basic concepts
127
7.5.2
Bit-stuffing in two dimensions
128
7.6
Pickard random fields
128
7.6.1
General Pickard random fields
129
7.6.2
Remarks on causal models
130
7.7
Markov random fields with maximum entropy
131
7.8
Block Pickard construction
132
7.8.1
Constructing Pickard random fields from two Markov
chains
133
7.8.2
Block Pickard random fields for two-dimensional
constraints
136
7.8.3
Block Pickard random fields
-
no isolated bit
137
7.8.4
Tiling with dominoes using Pickard random fields
140
7.9
Notes
142
Exercises
143
References
145
Reed-Solomon codes in applications
146
8.1
Introduction
146
8.2
Binary images of Reed-Solomon codes
146
8.3
Concatenated codes
148
8.4
Product codes
149
8.5
Iterated decoding of product codes
150
8.6
Graph codes for two-dimensional error-correction
152
8.6.1
Bipartite graphs from geometries
153
8.6.2
Minimum distances of graph codes
154
8.6.3
Graph codes as two-dimensional arrays
155
8.7
Errors in two-dimensional media
155
8.7.1
Defects in physical media or in the writing/printing
process
155
Contents
8.7.2 Degradation
of the media in use
8.7.3
Degradation due to loss of alignment or synchronization
8.8
Notes
Exercises
156
156
156
157
Appendix A Fast arithmetic coding
Appendix
В
Maximizing entropy
Appendix
С
Decoding of Reed-Solomon code in
F
(16)
Index
158
160
163
170
|
any_adam_object | 1 |
author | Justesen, Jørn 1944-2019 Forchhammer, Søren |
author_GND | (DE-588)128905042 (DE-588)139621490 |
author_facet | Justesen, Jørn 1944-2019 Forchhammer, Søren |
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callnumber-first | Q - Science |
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callnumber-raw | QA268 |
callnumber-search | QA268 |
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classification_rvk | ST 152 |
ctrlnum | (OCoLC)320802735 (DE-599)BVBBV035806734 |
dewey-full | 005.7/2 |
dewey-hundreds | 000 - Computer science, information, general works |
dewey-ones | 005 - Computer programming, programs, data, security |
dewey-raw | 005.7/2 |
dewey-search | 005.7/2 |
dewey-sort | 15.7 12 |
dewey-tens | 000 - Computer science, information, general works |
discipline | Informatik |
edition | 1. publ. |
format | Book |
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spelling | Justesen, Jørn 1944-2019 Verfasser (DE-588)128905042 aut Two-dimensional information theory and coding with application to graphics and high-density storage media Jørn Justesen and Søren Forchhammer 1. publ. Cambridge Cambridge Univ. Press 2010 IX, 171 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematik Mathematisches Modell Coding theory Information storage and retrieval systems Mathematics Bipartite graphs Computer storage devices Mathematical models Computer graphics Mathematics Data visualization Binary system (Mathematics) Speichermedien (DE-588)4351464-9 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Bipartiter Graph (DE-588)4145661-0 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Dimension 2 (DE-588)4321721-7 gnd rswk-swf Informationstheorie (DE-588)4026927-9 s Dimension 2 (DE-588)4321721-7 s Bipartiter Graph (DE-588)4145661-0 s Speichermedien (DE-588)4351464-9 s Codierungstheorie (DE-588)4139405-7 s DE-604 Forchhammer, Søren Verfasser (DE-588)139621490 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018665749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Justesen, Jørn 1944-2019 Forchhammer, Søren Two-dimensional information theory and coding with application to graphics and high-density storage media Mathematik Mathematisches Modell Coding theory Information storage and retrieval systems Mathematics Bipartite graphs Computer storage devices Mathematical models Computer graphics Mathematics Data visualization Binary system (Mathematics) Speichermedien (DE-588)4351464-9 gnd Informationstheorie (DE-588)4026927-9 gnd Bipartiter Graph (DE-588)4145661-0 gnd Codierungstheorie (DE-588)4139405-7 gnd Dimension 2 (DE-588)4321721-7 gnd |
subject_GND | (DE-588)4351464-9 (DE-588)4026927-9 (DE-588)4145661-0 (DE-588)4139405-7 (DE-588)4321721-7 |
title | Two-dimensional information theory and coding with application to graphics and high-density storage media |
title_auth | Two-dimensional information theory and coding with application to graphics and high-density storage media |
title_exact_search | Two-dimensional information theory and coding with application to graphics and high-density storage media |
title_full | Two-dimensional information theory and coding with application to graphics and high-density storage media Jørn Justesen and Søren Forchhammer |
title_fullStr | Two-dimensional information theory and coding with application to graphics and high-density storage media Jørn Justesen and Søren Forchhammer |
title_full_unstemmed | Two-dimensional information theory and coding with application to graphics and high-density storage media Jørn Justesen and Søren Forchhammer |
title_short | Two-dimensional information theory and coding |
title_sort | two dimensional information theory and coding with application to graphics and high density storage media |
title_sub | with application to graphics and high-density storage media |
topic | Mathematik Mathematisches Modell Coding theory Information storage and retrieval systems Mathematics Bipartite graphs Computer storage devices Mathematical models Computer graphics Mathematics Data visualization Binary system (Mathematics) Speichermedien (DE-588)4351464-9 gnd Informationstheorie (DE-588)4026927-9 gnd Bipartiter Graph (DE-588)4145661-0 gnd Codierungstheorie (DE-588)4139405-7 gnd Dimension 2 (DE-588)4321721-7 gnd |
topic_facet | Mathematik Mathematisches Modell Coding theory Information storage and retrieval systems Mathematics Bipartite graphs Computer storage devices Mathematical models Computer graphics Mathematics Data visualization Binary system (Mathematics) Speichermedien Informationstheorie Bipartiter Graph Codierungstheorie Dimension 2 |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018665749&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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