Convolutional Coding: Fundamentals and Applications L. H. Charles Lee Artech House Boston London
Contents Preface xi Chapter 1 Introduction of Coded Digital Communication Systems 1 1.1 Introduction 1 1.2 Elements of a Digital Communication System 2 1.2.1 Data Source and Data Sink 2 1.2.2 Channel Encoder and Channel Decoder 2 1.2.3 Modulator, Transmission Path, and Demodulator 3 1.2.4 Channel Models 7 References 10 Chapter 2 Structures of Convolutional Codes 11 2.1 Encoding and Mathematical Model of Convolutional Codes 11 2.2 Polynomial Matrix Representation of Convolutional Codes 19 2.3 Error Propagation Effect and Code Design 24 2.3.1 Algebraic Structures of Generator Polynomial Matrix G(D) 30 2.3.2 Algebraic Structures of Syndrome-Former Polynomial Matrix H T (D) 33 2.3.3 Systematic Convolutional Encoder With Feedback 36 2.4 Graphical Representations of Convolutional Codes 40 2.4.1 Encoder Tree and Trellis Diagrams 40 2.4.2 Encoder State Diagram 43 2.4.3 Syndrome-Former Trellis Diagram 44 2.5 Distance Properties of Convolutional Codes 47 2.6 Generating Function of Convolutional Codes 51 References 55 VII
viii Convolutional Coding: Fundamentals and Applications Chapter 3 Suboptimal and Optimal Decoding of Convolutional Codes 57 3.1 Introduction 57 3.2 Sliding Block Decoding 59 3.3 Maximum-Likelihood Viterbi Algorithm Decoding 63 3.3.1 Hard-Decision Viterbi Algorithm Decoding 64 3.3.2 Soft-Decision Viterbi Algorithm Decoding 70 3.4 Syndrome-Former Trellis Decoding 73 3.5 Scarce-State-Transition-Type Viterbi Algorithm Decoding 74 3.6 Scarce-State-Transition-Type Syndrome-Former Trellis Decoding 79 3.7 Performance of Hard-Decision Maximum-Likelihood Decoding 80 3.8 Performance of Soft-Decision Maximum-Likelihood Decoding 83 3.9 Computer Simulation Results and Discussion 84 References 87 Chapter 4 Sequential Decoding of Convolutional Codes 89 4.1 Introduction 89 4.2 Fano Metric 89 4.3 Stack Algorithm Decoding 91 4.4 Fano Algorithm Decoding 92 References 100 Chapter 5 Encoding and Decoding of Punctured Convolutional Codes 101 5.1 Introduction 101 5.2 Encoding of Punctured Convolutional Codes 101 5.3 Maximum-Likelihood Decoding of Punctured Convolutional Codes 105 5.4 Performance of Punctured Convolutional Codes 109 5.5 Concept of Rate-Compatible Punctured Convolutional Codes 110 5.6 Maximum-Likelihood Decoding of Rate-Compatible Punctured Convolutional Codes 111 5.7 Computer Simulation Results and Discussion 112 References 115 Chapter 6 Majority-Logic Decoding of Convolutional Codes 117 6.1 Introduction 117
Contents ix 6.2 Hard-Decision Majority-Logic Decoding 118 6.2.1 Majority-Logic Definite Decoding 123 6.2.2 Majority-Logic Feedback Decoding 131 6.3 Error Propagation Effect 139 6.4 Performance of Hard-Decision Majority-Logic Decoding 141 6.5 Soft-Decision Majority-Logic Decoding 141 6.6 Computer Simulation Results 143 References 146 Chapter 7 Combined Convolutional Coding and Modulation 149 7.1 Introduction 149 7.2 Two-Dimensional Trellis-Coded Modulation 154 7.2.1 Phase-Invariant Convolutional Codes 160 7.2.2 90 Degree Phase-Invariant Convolutional Codes 163 7.3 Multidimensional Lattice Trellis-Coded Modulation 167 7.3.1 Partitioning of Multidimensional Lattices 168 7.3.2 Signal Mapping Rules and Phase-Invariant Code Construction 175 7.3.3 Multidimensional Viterbi Algorithm Decoding 181 7.3.4 Advantages of Using 2iV-Dimensional Lattice TCM Scheme 184 7.4 Multidimensional M-PSK Trellis-Coded Modulation 185 7.4.1 Partitioning of Multidimensional M-PSK Constellations 186 7.4.2 Four-Dimensional M-PSK TCM: Signal Mapping Rules and Phase-Invariant Code Construction 191 7.4.3 Eight-Dimensional M-PSK TCM: Signal Mapping Rules and Phase-Invariant Code Construction 194 7.4.4 Multidimensional Viterbi Algorithm Decoding 198 7.4.5 Advantages of Using Multidimensional M-PSK TCM Scheme 204 References 205 Chapter 8 Combined Coding, Modulation, and Equalization 209 8.1 Introduction 209 8.2 Nonlinear (Decision-Feedback) Equalizer 210 8.3 Coded System Model and Assumptions 213 8.4 Combined Trellis Diagram 215 8.4.1 Full-State Combined Trellis 216 8.4.2 Reduced-State Combined Trellis 217 8.5 Combined Equalization and Trellis Decoding 218
x Convolutional Coding: Fundamentals and Applications 8.6 Computer Simulation Results 219 References 222 Chapter 9 Applications of Convolutional Codes 225 9.1 Introduction 225 9.2 Applications to Space Communications 225 9.2.1 Pioneer Missions 225 9.2.2 Voyager Mission 226 9.2.3 Galileo Mission 228 9.3 Applications to Satellite Communications 229 9.4 Applications to Mobile Communications 230 9.4.1 GSM Digital Radio System 230 9.5 Applications to Voice-Band Data Communications 236 References 243 Appendix A Appendix B Appendix C Appendix D Appendix E Connection Vectors of Convolutional Codes for Viterbi Decoding 245 Connection Vectors of Convolutional Codes for Sequential Decoding 249 Puncturing Matrix for Punctured and Rate-Compatible Punctured Convolutional Codes 251 Generator Polynomials for Self-Orthogonal Systematic Convolutional Codes 263 Generator Polynomial Matrix for Two-Dimensional Linear Trellis Codes 265 Appendix F Encoder Trellis Program 269 Appendix G Viterbi Codec Programs 283 About the Author 307 Index 309