Modern coding theory:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
Ausgabe: | 1. publ. |
Schlagworte: | |
Online-Zugang: | Verlagsmeldung Inhaltsverzeichnis Inhaltsverzeichnis |
Beschreibung: | Includes bibliographical references and index. - Includes Internet access |
Beschreibung: | XVI, 572 S. graph. Darst. |
ISBN: | 9780521852296 0521852293 |
Internformat
MARC
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245 | 1 | 0 | |a Modern coding theory |c Tom Richardson ; Ruediger Urbanke |
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264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
300 | |a XVI, 572 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
500 | |a Includes bibliographical references and index. - Includes Internet access | ||
650 | 7 | |a Codering |2 gtt | |
650 | 7 | |a Dataprocessing |2 gtt | |
650 | 4 | |a Coding theory | |
650 | 0 | 7 | |a Codierungstheorie |0 (DE-588)4139405-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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adam_text | Titel: Modern coding theory
Autor: Richardson, Thomas J.
Jahr: 2008
CONTENTS
Preface • pagexiii
1 Introduction ¦ page i
§1.1 Why You Should Read This Book • i
§1.2 Communications Problem • 2
§1.3 Coding: Trial and Error ¦ 4
§1.4 Codes and Ensembles • 5
§1.5 MAP and ML Decoding and APP Processing ¦ 9
§1.6 Channel Coding Theorem ¦ 9
§1.7 Linear Codes and Complexity • 13
§1.8 Rate, Probability, Complexity, and Length • 18
§1.9 Tour of Iterative Decoding • 23
§1.10 Notation, Conventions, and Useful Facts • 27
Notes • 32
Problems • 35
References • 44
2 Factor Graphs • page 49
§2.1 Distributive Law • 49
§2.2 Graphical Representation of Factorizations • 50
§2.3 Recursive Determination of Marginals • 51
§2.4 Marginalization via Message Passing • 54
§2.5 Decoding via Message Passing ¦ 57
§2.6 Limitations of Cycle-Free Codes ¦ 64
§2.7 Message Passing on Codes with Cycles • 65
Notes • 65
Problems • 67
References • 68
3 Binary Erasure Channel • page 71
§3.1 Channel Model • 71
§3.2 Transmission via Linear Codes ¦ 72
§3.3 Tanner Graphs • 75
§3.4 Low-Density Parity-Check Codes • 76
§3.5 Message-Passing Decoder • 82
vu
Vili CONTENTS
§3.6 Two Basic Simplifications • 83
§3.7 Computation Graph and Tree Ensemble • 87
§3.8 Tree Channel and Convergence to Tree Channel • 94
§3.9 Density Evolution • 95
§3.10 Monotonicity • 96
§3.11 Threshold • 97
§3.12 Fixed Point Characterization of Threshold • 98
§3.13 Stability • 100
§3.14 EXIT Charts • 101
§3.15 Capacity-Achieving Degree Distributions • 108
§3.16 Gallager s Lower Bound on Density • 111
§3.17 Optimally Sparse Degree Distribution Pairs • 113
§3.18 Degree Distributions with Given Maximum Degree • 114
§3.19 Peeling Decoder and Order of Limits • 115
§3.20 EXIT Function and MAP Performance • 122
§3.21 Maxwell Decoder • 131
§3.22 Exact Finite-Length Analysis • 134
§3.23 Finite-Length Scaling • 143
§3.24 Weight Distribution and Error Floor • 148
Notes • 156
Problems • 160
References • 169
4 Binary Memoryless Symmetric Channels • page 175
§4.1 Basic Definitions and Examples • 175
§4.2 Message-Passing Decoder • 209
§4.3 Two Basic Simplifications • 214
§4.4 Tree Channel and Convergence to Tree Channel • 216
§4.5 Density Evolution ¦ 217
§4.6 Monotonicity • 221
§4.7 Threshold ¦ 226
§4.8 Fixed Point Characterization of Threshold • 226
§4.9 Stability • 230
§4.10 EXIT Charts • 234
§4.11 Gallager s Lower Bound on Density ¦ 245
§4.12 GEXIT Function and MAP Performance • 249
§4.13 Finite-Length Scaling • 257
§4.14 Error Floor under MAP Decoding • 258
IX
Notes • 261
Problems • 267
References ¦ 283
5 General Channels • page 291
§5.1 Fading Channel • 291
§5.2 Z Channel ¦ 294
§5.3 Channels with Memory ¦ 297
§5.4 Coding for High Spectral Efficiency • 303
§5.5 Multiple-Access Channel • 308
Notes ¦ 312
Problems • 314
References • 316
6 Turbo Codes • page 323
§6.1 Convolutional Codes • 323
§6.2 Structure and Encoding • 334
§6.3 Decoding ¦ 336
§6.4 Basic Simplifications • 339
§6.5 Density Evolution • 341
§6.6 Stability Condition ¦ 344
§6.7 EXIT Charts • 346
§6.8 GEXIT Function and MAP Performance • 347
§6.9 Weight Distribution and Error Floor ¦ 349
§6.10 Variations on the Theme • 363
Notes • 365
Problems • 369
References • 375
7 General Ensembles • page 381
§7.1 Multi-Edge-Type LDPC Code Ensembles • 382
§7.2 Multi-Edge-Type LDPC Codes: Analysis • 389
§7.3 Structured Codes • 397
§7.4 Non-Binary Codes • 405
§7.5 Low-Density Generator Codes and Rateless Codes • 410
Notes • 418
Problems • 421
References • 421
X CONTENTS
8 Expander Codes and Flipping Algorithm • page 427
§8.1 Building Codes from Expanders • 427
§8.2 Flipping Algorithm • 428
§8.3 Bound on Expansion of a Graph • 429
§8.4 Expansion of a Random Graph • 431
Notes ¦ 434
Problems • 435
References • 435
A Encoding Low-Density Parity-Check Codes • page 437
§A.i Encoding Generic LDPC Codes • 437
§A.2 Greedy Upper Triangulation • 443
§A.3 Linear Encoding Complexity • 448
§A.4 Analysis of Asymptotic Gap • 452
Notes • 456
Problems • 456
References • 457
B Efficient Implementation of Density Evolution • page 459
§B.i Quantization • 460
§B.2 Variable-Node Update via Fourier Transform • 460
§B.3 Check-Node Update via Table Method ¦ 462
§B.4 Check-Node Update via Fourier Method • 464
Notes • 477
Problems • 477
References ¦ 478
C Concentration Inequalities • page 479
§C.i First and Second Moment Method • 480
§C.2 Bernstein s Inequality • 482
§C.3 Martingales • 484
§C.4 Wormald s Differential Equation Approach • 490
§C.5 Convergence to Poisson Distribution ¦ 497
Notes • 500
Problems ¦ 501
References • 502
D Formal Power Sums • page 505
§D.i Definition • 505
§D.2 Basic Properties • 505
XI
§D.3 Summation of Subsequences ¦ 506
§D.4 Coefficient Growth of Powers of Polynomials • 507
§D.5 Unimodality • 529
Notes • 529
Problems • 530
References • 535
E Convexity, Degradation, and Stability • page 537
Authors • page 551
Index • page 559
|
adam_txt |
Titel: Modern coding theory
Autor: Richardson, Thomas J.
Jahr: 2008
CONTENTS
Preface • pagexiii
1 Introduction ¦ page i
§1.1 Why You Should Read This Book • i
§1.2 Communications Problem • 2
§1.3 Coding: Trial and Error ¦ 4
§1.4 Codes and Ensembles • 5
§1.5 MAP and ML Decoding and APP Processing ¦ 9
§1.6 Channel Coding Theorem ¦ 9
§1.7 Linear Codes and Complexity • 13
§1.8 Rate, Probability, Complexity, and Length • 18
§1.9 Tour of Iterative Decoding • 23
§1.10 Notation, Conventions, and Useful Facts • 27
Notes • 32
Problems • 35
References • 44
2 Factor Graphs • page 49
§2.1 Distributive Law • 49
§2.2 Graphical Representation of Factorizations • 50
§2.3 Recursive Determination of Marginals • 51
§2.4 Marginalization via Message Passing • 54
§2.5 Decoding via Message Passing ¦ 57
§2.6 Limitations of Cycle-Free Codes ¦ 64
§2.7 Message Passing on Codes with Cycles • 65
Notes • 65
Problems • 67
References • 68
3 Binary Erasure Channel • page 71
§3.1 Channel Model • 71
§3.2 Transmission via Linear Codes ¦ 72
§3.3 Tanner Graphs • 75
§3.4 Low-Density Parity-Check Codes • 76
§3.5 Message-Passing Decoder • 82
vu
Vili CONTENTS
§3.6 Two Basic Simplifications • 83
§3.7 Computation Graph and Tree Ensemble • 87
§3.8 Tree Channel and Convergence to Tree Channel • 94
§3.9 Density Evolution • 95
§3.10 Monotonicity • 96
§3.11 Threshold • 97
§3.12 Fixed Point Characterization of Threshold • 98
§3.13 Stability • 100
§3.14 EXIT Charts • 101
§3.15 Capacity-Achieving Degree Distributions • 108
§3.16 Gallager's Lower Bound on Density • 111
§3.17 Optimally Sparse Degree Distribution Pairs • 113
§3.18 Degree Distributions with Given Maximum Degree • 114
§3.19 Peeling Decoder and Order of Limits • 115
§3.20 EXIT Function and MAP Performance • 122
§3.21 Maxwell Decoder • 131
§3.22 Exact Finite-Length Analysis • 134
§3.23 Finite-Length Scaling • 143
§3.24 Weight Distribution and Error Floor • 148
Notes • 156
Problems • 160
References • 169
4 Binary Memoryless Symmetric Channels • page 175
§4.1 Basic Definitions and Examples • 175
§4.2 Message-Passing Decoder • 209
§4.3 Two Basic Simplifications • 214
§4.4 Tree Channel and Convergence to Tree Channel • 216
§4.5 Density Evolution ¦ 217
§4.6 Monotonicity • 221
§4.7 Threshold ¦ 226
§4.8 Fixed Point Characterization of Threshold • 226
§4.9 Stability • 230
§4.10 EXIT Charts • 234
§4.11 Gallager's Lower Bound on Density ¦ 245
§4.12 GEXIT Function and MAP Performance • 249
§4.13 Finite-Length Scaling • 257
§4.14 Error Floor under MAP Decoding • 258
IX
Notes • 261
Problems • 267
References ¦ 283
5 General Channels • page 291
§5.1 Fading Channel • 291
§5.2 Z Channel ¦ 294
§5.3 Channels with Memory ¦ 297
§5.4 Coding for High Spectral Efficiency • 303
§5.5 Multiple-Access Channel • 308
Notes ¦ 312
Problems • 314
References • 316
6 Turbo Codes • page 323
§6.1 Convolutional Codes • 323
§6.2 Structure and Encoding • 334
§6.3 Decoding ¦ 336
§6.4 Basic Simplifications • 339
§6.5 Density Evolution • 341
§6.6 Stability Condition ¦ 344
§6.7 EXIT Charts • 346
§6.8 GEXIT Function and MAP Performance • 347
§6.9 Weight Distribution and Error Floor ¦ 349
§6.10 Variations on the Theme • 363
Notes • 365
Problems • 369
References • 375
7 General Ensembles • page 381
§7.1 Multi-Edge-Type LDPC Code Ensembles • 382
§7.2 Multi-Edge-Type LDPC Codes: Analysis • 389
§7.3 Structured Codes • 397
§7.4 Non-Binary Codes • 405
§7.5 Low-Density Generator Codes and Rateless Codes • 410
Notes • 418
Problems • 421
References • 421
X CONTENTS
8 Expander Codes and Flipping Algorithm • page 427
§8.1 Building Codes from Expanders • 427
§8.2 Flipping Algorithm • 428
§8.3 Bound on Expansion of a Graph • 429
§8.4 Expansion of a Random Graph • 431
Notes ¦ 434
Problems • 435
References • 435
A Encoding Low-Density Parity-Check Codes • page 437
§A.i Encoding Generic LDPC Codes • 437
§A.2 Greedy Upper Triangulation • 443
§A.3 Linear Encoding Complexity • 448
§A.4 Analysis of Asymptotic Gap • 452
Notes • 456
Problems • 456
References • 457
B Efficient Implementation of Density Evolution • page 459
§B.i Quantization • 460
§B.2 Variable-Node Update via Fourier Transform • 460
§B.3 Check-Node Update via Table Method ¦ 462
§B.4 Check-Node Update via Fourier Method • 464
Notes • 477
Problems • 477
References ¦ 478
C Concentration Inequalities • page 479
§C.i First and Second Moment Method • 480
§C.2 Bernstein's Inequality • 482
§C.3 Martingales • 484
§C.4 Wormald's Differential Equation Approach • 490
§C.5 Convergence to Poisson Distribution ¦ 497
Notes • 500
Problems ¦ 501
References • 502
D Formal Power Sums • page 505
§D.i Definition • 505
§D.2 Basic Properties • 505
XI
§D.3 Summation of Subsequences ¦ 506
§D.4 Coefficient Growth of Powers of Polynomials • 507
§D.5 Unimodality • 529
Notes • 529
Problems • 530
References • 535
E Convexity, Degradation, and Stability • page 537
Authors • page 551
Index • page 559 |
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spelling | Richardson, Tom Verfasser aut Modern coding theory Tom Richardson ; Ruediger Urbanke 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XVI, 572 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index. - Includes Internet access Codering gtt Dataprocessing gtt Coding theory Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s DE-604 Urbanke, Rüdiger Verfasser aut http://www.loc.gov/catdir/enhancements/fy0808/2007039544-d.html lizenzfrei Verlagsmeldung http://www.loc.gov/catdir/enhancements/fy0808/2007039544-t.html lizenzfrei Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016485105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Richardson, Tom Urbanke, Rüdiger Modern coding theory Codering gtt Dataprocessing gtt Coding theory Codierungstheorie (DE-588)4139405-7 gnd |
subject_GND | (DE-588)4139405-7 |
title | Modern coding theory |
title_auth | Modern coding theory |
title_exact_search | Modern coding theory |
title_exact_search_txtP | Modern coding theory |
title_full | Modern coding theory Tom Richardson ; Ruediger Urbanke |
title_fullStr | Modern coding theory Tom Richardson ; Ruediger Urbanke |
title_full_unstemmed | Modern coding theory Tom Richardson ; Ruediger Urbanke |
title_short | Modern coding theory |
title_sort | modern coding theory |
topic | Codering gtt Dataprocessing gtt Coding theory Codierungstheorie (DE-588)4139405-7 gnd |
topic_facet | Codering Dataprocessing Coding theory Codierungstheorie |
url | http://www.loc.gov/catdir/enhancements/fy0808/2007039544-d.html http://www.loc.gov/catdir/enhancements/fy0808/2007039544-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016485105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT richardsontom moderncodingtheory AT urbankerudiger moderncodingtheory |
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