Trellis and turbo coding

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Title:

Personal Author:

Schlegel, Christian

Publication Information:

Piscataway, NJ : IEEE Press, 2004

ISBN:

9780471227557

Subject Term:

Error-correcting codes (Information theory)

Trellis-coded modulation

Digital communications

Added Author:

Perez, Lance

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000003593484	TK5102.96 S33 2004	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000010150306	TK5102.96 S33 2004	Open Access Book	Book	Searching... Unknown

Trellis and turbo coding are used to compress and clean communications signals to allow greater bandwidth and clarity Presents the basics, theory, and applications of these techniques with a focus on potential standard state-of-the art methods in the future Provides a classic basis for anyone who works in the area of digital communications

A Wiley-IEEE Press Publication

Author Notes

Christian B. Schlegel, PhD, is iCORE Professor of Digital Communications at the University of Alberta, Canada
Lance C. Perez, PhD, is currently a member of the faculty in the Department of Electrical Engineering at the University of Nebraska in Lincoln, Nebraska

Preface	p. xiii
1 Introduction	p. 1
1.1 Modern Digital Communications	p. 1
1.2 The Rise of Digital Communications	p. 2
1.3 Communication Systems	p. 3
1.4 Error Control Coding	p. 5
1.5 Bandwidth, Power, and Complexity	p. 10
1.6 A Brief History--The Drive Toward Capacity	p. 18
Bibliography	p. 20
2 Communication Theory Basics	p. 25
2.1 The Probabilistic Viewpoint	p. 25
2.2 Vector Communication Channels	p. 26
2.3 Optimum Receivers	p. 29
2.4 Matched Filters	p. 31
2.5 Message Sequences	p. 32
2.6 The Complex Equivalent Baseband Model	p. 36
2.7 Spectral Behavior	p. 40
2.8 Multiple Antenna Channels (MIMO Channels)	p. 42
Appendix 2.A	p. 47
Bibliography	p. 49
3 Trellis-Coded Modulation	p. 51
3.1 An Introductory Example	p. 51
3.2 Group-Trellis Codes	p. 55
3.3 The Mapping Function	p. 57
3.4 Construction of Codes	p. 60
3.5 Lattices	p. 65
3.6 Lattice Formulation of Trellis Codes	p. 71
3.7 Rotational Invariance	p. 77
3.8 V.fast	p. 83
3.9 Geometric Uniformity	p. 85
3.10 Historical Notes	p. 92
Bibliography	p. 92
4 Convolutional Codes	p. 95
4.1 Convolutional Codes as Binary Trellis Codes	p. 95
4.2 Codes and Encoders	p. 97
4.3 Fundamental Theorems from Basic Algebra	p. 103
4.4 Systematic Encoders	p. 113
4.5 Systematic Feedback and Recursive Systematic Encoder Realizations	p. 115
4.6 Maximum Free-Distance Convolutional Codes	p. 117
Appendix 4.A	p. 121
Bibliography	p. 122
5 Link to Block Codes	p. 125
5.1 Preliminaries	p. 125
5.2 Block Code Primer	p. 126
5.3 Trellis Description of Block Codes	p. 127
5.4 Minimal Trellises	p. 128
5.5 Minimum-Span Generator Matrices	p. 133
5.6 Construction of the PC Trellis	p. 136
5.7 Tail-Biting Trellises	p. 138
5.8 The Squaring Construction and the Trellis of Lattices	p. 141
5.9 The Construction of Reed-Muller Codes	p. 147
5.10 A Decoding Example	p. 149
Bibliography	p. 152
6 Performance Bounds	p. 155
6.1 Error Analysis	p. 155
6.2 The Error Event Probability	p. 155
6.3 Finite-State Machine Description of Error Events	p. 160
6.4 The Transfer Function Bound	p. 163
6.5 Reduction Theorems	p. 166
6.6 Random Coding Bounds	p. 170
Appendix 6.A	p. 180
Appendix 6.B	p. 180
Bibliography	p. 181
7 Decoding Strategies	p. 183
7.1 Background and Introduction	p. 183
7.2 Tree Decoders	p. 184
7.3 The Stack Algorithm	p. 187
7.4 The Fano Algorithm	p. 188
7.5 The M-Algorithm	p. 190
7.6 Maximum Likelihood Decoding	p. 200
7.7 A Posteriori Probability Symbol Decoding	p. 203
7.8 Log-APP and Approximations	p. 209
7.9 Random Coding Analysis of Sequential Decoding	p. 213
7.10 Some Final Remarks	p. 218
Appendix 7.A	p. 219
Bibliography	p. 223
8 Factor Graphs	p. 227
8.1 Factor Graphs: Introduction and History	p. 227
8.2 Graphical Function Representation	p. 228
8.3 The Sum-Product Algorithm	p. 231
8.4 Iterative Probability Propagation	p. 232
8.5 The Factor Graph of Trellises	p. 235
8.6 Exactness of the Sum-Product Algorithm for Trees	p. 238
8.7 Binary Factor Graphs	p. 242
Variable Node Messages	p. 242
Parity-Check Node Messages	p. 243
Log Likelihood Ratio (LLR)	p. 243
LLR Variable Node Messages	p. 243
LLR Check Node Messages	p. 244
8.8 Normal Factor Graphs	p. 245
Symbol Variable Replication	p. 246
State Variable Replication	p. 247
Bibliography	p. 247
9 Low-Density Parity-Check Codes	p. 251
9.1 Introduction	p. 251
9.2 LDPC Codes and Graphs	p. 252
9.3 Message Passing Decoding Algorithms	p. 255
9.4 Density Evolution	p. 259
9.5 Density Evolution for Binary Erasure Channels	p. 260
9.6 Binary Symmetric Channels and the Gallager Algorithms	p. 265
9.7 The AWGN Channel	p. 269
9.8 LDPC Encoding	p. 275
9.9 Encoding via Message-Passing	p. 277
9.10 Repeat Accumulate Codes on Graphs	p. 280
Bibliography	p. 283
10 Parallel Concatenation (Turbo Codes)	p. 285
10.1 Introduction	p. 285
10.2 Parallel Concatenated Convolutional Codes	p. 287
10.3 Distance Spectrum Analysis of Turbo Codes	p. 290
10.4 The Free Distance of a Turbo Code	p. 292
10.5 The Distance Spectrum of a Turbo Code	p. 297
10.6 Weight Enumerator Analysis of Turbo Codes	p. 300
10.7 Iterative Decoding of Turbo Codes	p. 307
10.8 EXIT Analysis	p. 310
10.9 Interleavers	p. 317
10.10 Turbo Codes in Telecommunication Standards	p. 320
10.10.1 The Space Data System Standard	p. 320
10.10.2 3G Wireless Standards	p. 322
10.10.3 Digital Video Broadcast Standards	p. 323
10.11 Epilog	p. 324
Bibliography	p. 325
11 Serial Concatenation	p. 329
11.1 Introduction	p. 329
11.2 An Introductory Example	p. 330
11.3 Weight Enumerator Analysis of SCCCs	p. 331
11.3.1 Design Rule Examples	p. 338
11.4 Iterative Decoding and Performance of SCCCs	p. 341
11.4.1 Performance of SCCCs and PCCCs	p. 343
11.5 EXIT Analysis of Serially Concatenated Codes	p. 344
11.6 Conclusion	p. 348
Bibliography	p. 348
12 Turbo-Coded Modulation	p. 351
12.1 Introduction	p. 351
12.2 Turbo-Trellis-Coded Modulation (TTCM)	p. 351
12.3 Serial Concatenation	p. 355
12.4 EXIT Analysis	p. 356
12.5 Differential-Coded Modulation	p. 358
12.6 Concatenated Space-Time Coding	p. 363
12.7 Product Codes and Block Turbo Decoding	p. 368
12.8 Approximate APP Decoding	p. 369
12.9 Product Codes with High-Order Modulations	p. 372
12.10 The IEEE 802.16 Standard	p. 374
Bibliography	p. 375
Index	p. 379

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