Trellis and turbo coding

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 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.