Trellis and turbo coding

✍ Scribed by Schlegel, Christian; Perez, Lance

• Publisher: IEEE Press ; Hoboken
• Year: 2004
• Tongue: English
• Leaves: 521
• Series: IEEE series on mobile & digital communication
• Category: Library

✦ Synopsis

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.

Abstract: 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

✦ Table of Contents

Content: 1. Introduction --
1.1. Modern Digital Communications --
1.2. The Rise of Digital Communications --
1.3. Communication Systems --
1.4. Error Control Coding --
1.5. Bandwidth, Power, and Complexity --
1.6. A Brief History--The Drive Toward Capacity --
2. Communication Theory Basics --
2.1. The Probabilistic Viewpoint --
2.2. Vector Communication Channels --
2.3. Optimum Receivers --
2.4. Matched Filters --
2.5. Message Sequences --
2.6. The Complex Equivalent Baseband Moel --
2.7. Spectral Behavior --
2.8. Multiple Antenna Channels (MIMO Channels) --
Appendix 2.A --
3. Trellis-Coded Modulation --
3.1. An Introductory Example --
3.2. Group-Trellis Codes --
3.3. The Mapping Function --
3.4. Construction of Codes --
3.5. Lattices --
3.6. Lattice Formulation of Trellis Codes --
3.7. Rotational Invariance --
3.8. V.fast --
3.9. Geometric Uniformity --
3.10. Historical Notes --
4. Convolutional Codes --
4.1. Convolutional Codes as Binary Trellis Codes --
4.2. Codes and Encoders --
4.3. Fundamental Theorems from Basic Algebra --
4.4. Systematic Encoders --
4.5. Systematic Feedback and Recursive Systematic Encoder Realizations --
4.6. Maximum Free-Distance Convolutional Codes --
Appendix 4.A --
5. Link to Block Codes --
5.1. Preliminaries --
5.2. Block Code Primer --
5.3. Trellis Description of Block Codes --
5.4. Minimal Trellises --
5.5. Minimum-Span Generator Matrices --
5.6. Construction of the PC Trellis --
5.7. Tail-Biting Trellises --
5.8. The Squaring Construction and the Trellis of Lattices --
5.9. The Construction of Reed-Muller Codes --
5.10. A Decoding Example --
6. Performance Bounds --
6.1. Error Analysis --
6.2. The Error Event Probability --
6.3. Finite-State Machine Description of Error Events --
6.4. The Transfer Function Bound --
6.5. Reduction Theorems --
6.6. Random Coding Bounds --
Appendix 6.A --
Appendix 6.B --
7. Decoding Strategies --
7.1. Background and Introduction --
7.2. Tree Decoders --
7.3. The Stack Algorithm --
7.4. The Fano Algorithm --
7.5. The M-Algorithm --
7.6. Maximum Likelihood Decoding --
7.7. A Posteriori Probability Symbol Decoding --
7.8. Log-APP and Approximations --
7.9. Random Coding Analysis of Sequential Decoding --
7.10. Some Final Remarks --
Appendix 7.A --
8. Factor Graphs --
8.1. Factor Graphs: Introduction and History --
8.2. Graphical Function Representation --
8.3. The Sum-Product Algorithm --
8.4. Iterative Probability Propagation --
8.5. The Factor Graph of Trellises --
8.6. Exactness of the Sum-Product Algorithm for Trees --
8.7. Binary Factor Graphs --
8.8. Normal Factor Graphs --
9. Low-Density Parity-Check Codes --
9.1. Introduction --
9.2. LDPC Codes and Graphs --
9.3. Message Passing Decoding Algorithms --
9.4. Density Evolution --
9.5. Density Evolution for Binary Erasure Channels --
9.6. Binary Symmetric Channels and the Gallager Algorithms --
9.7. The AWGN Channel --
9.8. LDPC Encoding --
9.9. Encoding via Message-Passing --
9.10. Repeat Accumulate Codes on Graphs --
10. Parallel Concatenation (Turbo Codes) --
10.1. Introduction --
10.2. Parallel Concatenated Convolutional Codes --
10.3. Distance Spectrum Analysis of Turbo Codes --
10.4. The Free Distance of a Turbo Code --
10.5. The Distance Spectrum of a Turbo Code --
10.6. Weight Enumerator Analysis of Turbo Codes --
10.7. Iterative Decoding of Turbo Codes --
10.8. EXIT Analysis --
10.9. Interleavers --
10.10. Turbo Codes in Telecommunication Standards --
10.11. Epilog --
11. Serial Concatenation --
11.1. Introduction --
11.2. An Introductory Example --
11.3. Weight Enumerator Analysis of SCCCs --
11.3.1. Design Rule Examples --
11.4. Iterative Decoding and Performance of SCCCs --
11.4.1. Performance of SCCCs and PCCCs --
11.5. EXIT Analysis of Serially Concatenated Codes --
11.6. Conclusion --
12. Turbo-Coded Modulation --
12.1. Introduction --
12.2. Turbo-Trellis-Coded Modulation (TTCM) --
12.3. Serial Concatenation --
12.4. EXIT Analysis --
12.5. Differential-Coded Modulation --
12.6. Concatenated Space-Time Coding --
12.7. Product Codes and Block Turbo Decoding --
12.8. Approximate APP Decoding --
12.9. Product Codes with High-Order Modulations --
12.10. The IEEE 802.16 Standard.