Title:
Trellis and turbo coding
Personal Author:
Publication Information:
Piscataway, NJ : IEEE Press, 2004
ISBN:
9780471227557
Added Author:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000003593484 | TK5102.96 S33 2004 | Open Access Book | Book | Searching... |
Searching... | 30000010150306 | TK5102.96 S33 2004 | Open Access Book | Book | Searching... |
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Summary
Summary
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
Table of Contents
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 |