Information theory and network coding:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2011
|
| Series: | Information technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 579 S. 24cm |
| ISBN: | 9781441946300 0387792333 9780387792330 9780387792347 |
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MARC
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Record in the Search Index
| _version_ | 1804143684659183616 |
|---|---|
| adam_text | Contents
The Science
of
Information................................ 1
Part I Components of Information Theory
2
Information Measures
..................................... 7
2.1
Independence and Markov Chains
......................... 7
2.2
Shannon s Information Measures
.......................... 12
2.3
Continuity of Shannon s Information Measures for Fixed
Finite Alphabets
........................................ 18
2.4
Chain Rules
............................................ 21
2.5
Informational Divergence
................................. 23
2.6
The Basic Inequalities
................................... 26
2.7
Some Useful Information Inequalities
....................... 28
2.8
Fano s Inequality
........................................ 32
2.9
Maximum Entropy Distributions
.......................... 36
2.10
Entropy Rate of a Stationary Source
....................... 38
Appendix
2.
A: Approximation of Random Variables with
Countably Infinite Alphabets by Truncation
................ 41
Chapter Summary
........................................... 43
Problems
................................................... 45
Historical Notes
............................................. 50
3
The i-Measure
............................................ 51
3.1
Preliminaries
............................................ 52
3.2
The /-Measure for Two Random Variables
.................. 53
3.3
Construction of the /-Measure
μ
......................... 55
3.4
μ*
Can Be Negative
..................................... 59
3.5
Information Diagrams
................................... 61
3.6
Examples of Applications
................................. 67
Appendix 3.A: A Variation of the Inclusion-Exclusion Formula
.... 74
Chapter Summary
........................................... 76
XVI Contents
Problems................................................... 78
Historical
Notes ............................................. 80
4
Zero-Error Data Compression
............................. 81
4.1
The Entropy Bound
..................................... 81
4.2
Prefix Codes
............................................ 86
4.2.1
Definition and Existence
........................... 86
4.2.2
Huffman Codes
................................... 88
4.3
Redundancy of Prefix Codes
.............................. 93
Chapter Summary
........................................... 97
Problems
................................................... 98
Historical Notes
............................................. 99
5
Weak Typicality
...........................................101
5.1
The Weak AEP
.........................................101
5.2
The Source Coding Theorem
..............................104
5.3
Efficient Source Coding
..................................106
5.4
The Shannon-McMillan-Breiman Theorem
.................107
Chapter Summary
...........................................109
Problems
...................................................110
Historical Notes
.............................................112
6
Strong Typicality
..........................................113
6.1
Strong AEP
............................................113
6.2
Strong Typicality Versus Weak Typicality
..................121
6.3
Joint Typicality
.........................................122
6.4
An Interpretation of the Basic Inequalities
..................131
Chapter Summary
...........................................131
Problems
...................................................132
Historical Notes
.............................................135
7
Discrete Memoryless Channels
............................137
7.1
Definition and Capacity
..................................141
7.2
The Channel Coding Theorem
............................149
7.3
The Converse
...........................................152
7.4
Achievability
............................................157
7.5
A Discussion
............................................164
7.6
Feedback Capacity
.......................................167
7.7
Separation of Source and Channel Coding
..................172
Chapter Summary
...........................................175
Problems
...................................................176
Historical Notes
.............................................181
8
Rate-Distortion Theory
....................................183
8.1
Single-Letter Distortion Measures
.........................184
8.2
The Rate-Distortion Function R(D)
.......................187
Contents XVII
8.3
The Rate-Distortion Theorem
.............................192
8.4
The Converse
...........................................200
8.5
Achievability of Ri(D)
...................................202
Chapter Summary
...........................................207
Problems
...................................................208
Historical Notes
.............................................209
9
The Blahut-Arimoto Algorithms
..........................211
9.1
Alternating Optimization
.................................212
9.2
The Algorithms
.........................................214
9.2.1
Channel Capacity
.................................214
9.2.2
The Rate-Distortion Function
.......................219
9.3
Convergence
............................................222
9.3.1
A Sufficient Condition
.............................222
9.3.2
Convergence to the Channel Capacity
................225
Chapter Summary
...........................................226
Problems
...................................................227
Historical Notes
.............................................228
10
Differential Entropy
.......................................229
10.1
Preliminaries
............................................231
10.2
Definition
..............................................235
10.3
Joint Differential Entropy, Conditional (Differential) Entropy,
and Mutual Information
..................................238
10.4
The AEP for Continuous Random Variables
................245
10.5
Informational Divergence
.................................248
10.6
Maximum Differential Entropy Distributions
................249
Chapter Summary
...........................................252
Problems
...................................................255
Historical Notes
.............................................256
11
Continuous-Valued Channels
..............................257
11.1
Discrete-Time Channels
..................................257
11.2
The Channel Coding Theorem
............................260
11.3
Proof of the Channel Coding Theorem
.....................262
11.3.1
The Converse
.....................................262
11.3.2
Achievability
......................................265
11.4
Memoryless Gaussian Channels
...........................270
11.5
Parallel Gaussian Channels
...............................272
11.6
Correlated Gaussian Channels
............................278
11.7
The Bandlimited White Gaussian Channel
..................280
11.8
The Bandlimited Colored Gaussian Channel
................287
11.9
Zero-Mean Gaussian Noise Is the Worst Additive Noise
.......290
Chapter Summary
...........................................294
Problems
...................................................296
Historical Notes
.............................................297
XVIII
Contents
12
Markov Structures
.........................................299
12.1
Conditional Mutual Independence
.........................300
12.2
Full Conditional Mutual Independence
.....................309
12.3
Markov Random Field
...................................314
12.4
Markov Chain
..........................................317
Chapter Summary
...........................................319
Problems
...................................................320
Historical Notes
.............................................321
13
Information Inequalities
...................................323
13.1
The Region
Г*п
..........................................325
13.2
Information Expressions in Canonical Form
.................326
13.3
A Geometrical Framework
...............................329
13.3.1
Unconstrained Inequalities
..........................329
13.3.2
Constrained Inequalities
............................330
13.3.3
Constrained Identities
..............................332
13.4
Equivalence of Constrained Inequalities
....................333
13.5
The Implication Problem of Conditional Independence
.......336
Chapter Summary
...........................................337
Problems
...................................................338
Historical Notes
.............................................338
14
Shannon-Type Inequalities
.................................339
14.1
The Elemental Inequalities
...............................339
14.2
A Linear Programming Approach
..........................341
14.2.1
Unconstrained Inequalities
..........................343
14.2.2
Constrained Inequalities and Identities
...............344
14.3
A Duality
..............................................345
14.4
Machine Proving
-
ITIP
.................................347
14.5
Tackling the Implication Problem
..........................351
14.6
Minimality of the Elemental Inequalities
....................353
Appendix
14.
A: The Basic Inequalities and the Polymatroidal
Axioms
................................................356
Chapter Summary
...........................................357
Problems
...................................................358
Historical Notes
.............................................360
15
Beyond Shannon-Type Inequalities
........................361
15.1
Characterizations of .T^,
Г$,
and
Г1*
......................361
15.2
A Non-Shannon-Type Unconstrained Inequality
.............369
15.3
A Non-Shannon-Type Constrained Inequality
...............374
15.4
Applications
............................................380
Chapter Summary
...........................................383
Problems
...................................................383
Historical Notes
.............................................385
Contents XIX
16
Entropy and Groups
.......................................387
16.1
Group Preliminaries
.....................................388
16.2
Group-Characterizable Entropy Functions
..................393
16.3
A Group Characterization of
Г*
..........................398
16.4
Information Inequalities and Group Inequalities
.............401
Chapter Summary
...........................................405
Problems
...................................................406
Historical Notes
.............................................408
Part II Fundamentals of Network Coding
17
Introduction
...............................................411
17.1
The Butterfly Network
...................................412
17.2
Wireless and Satellite Communications
.....................415
17.3
Source Separation
.......................................417
Chapter Summary
...........................................418
Problems
...................................................418
Historical Notes
.............................................419
18
The Max-Flow Bound
.....................................421
18.1
Point-to-Point Communication Networks
...................421
18.2
Examples Achieving the Max-Flow Bound
..................424
18.3
A Class of Network Codes
................................427
18.4
Proof of the Max-Flow Bound
.............................429
Chapter Summary
...........................................431
Problems
...................................................431
Historical Notes
.............................................434
19
Single-Source Linear Network Coding:
Acyclic Networks
..........................................435
19.1
Acyclic Networks
........................................436
19.2
Linear Network Codes
...................................437
19.3
Desirable Properties of a Linear Network Code
..............443
19.3.1
Transformation of a Linear Network Code
............447
19.3.2
Implementation of a Linear Network Code
............448
19.4
Existence and Construction
...............................449
19.5
Generic Network Codes
..................................460
19.6
Static Network Codes
....................................468
19.7
Random Network Coding: A Case Study
...................473
19.7.1
How the System Works
............................474
19.7.2
Model and Analysis
................................475
Chapter Summary
...........................................478
Problems
...................................................479
Historical Notes
.............................................482
XX
Contents
20
Single-Source
Linear Network
Coding: Cyclic
Networks.... 485
20.1
Delay-Free Cyclic Networks
...............................485
20.2
Convolutional Network Codes
.............................488
20.3
Decoding of Convolutional Network Codes
..................498
Chapter Summary
...........................................503
Problems
...................................................503
Historical Notes
.............................................504
21
Multi-source Network Coding
.............................505
21.1
The Max-Flow Bounds
...................................505
21.2
Examples of Application
.................................508
21.2.1
Multilevel Diversity Coding
.........................508
21.2.2
Satellite Communication Network
...................510
21.3
A Network Code for Acyclic Networks
.....................511
21.4
The Achievable Information Rate Region
...................512
21.5
Explicit Inner and Outer Bounds
..........................515
21.6
The Converse
...........................................516
21.7
Achievability
............................................521
21.7.1
Random Code Construction
........................524
21.7.2
Performance Analysis
..............................527
Chapter Summary
...........................................536
Problems
...................................................537
Historical Notes
.............................................539
Bibliography
...................................................541
Index
..........................................................561
|
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| author_GND | (DE-588)136373550 |
| author_facet | Yeung, Raymond W. 1962- |
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| bvnumber | BV036959889 |
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| ctrlnum | (OCoLC)706971257 (DE-599)BVBBV036959889 |
| discipline | Informatik |
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| id | DE-604.BV036959889 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:51:35Z |
| institution | BVB |
| isbn | 9781441946300 0387792333 9780387792330 9780387792347 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020874792 |
| oclc_num | 706971257 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG |
| owner_facet | DE-473 DE-BY-UBG |
| physical | XX, 579 S. 24cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Information technology |
| spelling | Yeung, Raymond W. 1962- Verfasser (DE-588)136373550 aut Information theory and network coding Raymond W. Yeung New York, NY Springer 2011 XX, 579 S. 24cm txt rdacontent n rdamedia nc rdacarrier Information technology Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 gnd rswk-swf Codierung (DE-588)4070059-8 gnd rswk-swf Rechnernetz (DE-588)4070085-9 gnd rswk-swf Netzwerktheorie (DE-588)4171531-7 s Codierungstheorie (DE-588)4139405-7 s Informationstheorie (DE-588)4026927-9 s DE-604 Rechnernetz (DE-588)4070085-9 s Codierung (DE-588)4070059-8 s 1\p DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yeung, Raymond W. 1962- Information theory and network coding Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd Netzwerktheorie (DE-588)4171531-7 gnd Codierung (DE-588)4070059-8 gnd Rechnernetz (DE-588)4070085-9 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4026927-9 (DE-588)4171531-7 (DE-588)4070059-8 (DE-588)4070085-9 |
| title | Information theory and network coding |
| title_auth | Information theory and network coding |
| title_exact_search | Information theory and network coding |
| title_full | Information theory and network coding Raymond W. Yeung |
| title_fullStr | Information theory and network coding Raymond W. Yeung |
| title_full_unstemmed | Information theory and network coding Raymond W. Yeung |
| title_short | Information theory and network coding |
| title_sort | information theory and network coding |
| topic | Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd Netzwerktheorie (DE-588)4171531-7 gnd Codierung (DE-588)4070059-8 gnd Rechnernetz (DE-588)4070085-9 gnd |
| topic_facet | Codierungstheorie Informationstheorie Netzwerktheorie Codierung Rechnernetz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT yeungraymondw informationtheoryandnetworkcoding |