| Contributors | p. v |
| Foreword | p. ix |
| Introduction | p. 1 |
| Digital messages | p. 3 |
| A first code | p. 4 |
| Hard input decoding and soft input decoding | p. 7 |
| Hard output decoding and soft output decoding | p. 11 |
| The performance measure | p. 11 |
| What is a good code? | p. 15 |
| Families of codes | p. 17 |
| Digital communications | p. 19 |
| Digital Modulations | p. 19 |
| Introduction | p. 19 |
| Linear Memoryless Modulations | p. 22 |
| Memoryless modulation with M states (M-FSK) | p. 29 |
| Modulations with memory by continuous phase frequency shift keying (CPFSK) | p. 31 |
| Structure and performance of the optimal receiver on a Gaussian channel | p. 37 |
| Structure of the coherent receiver | p. 37 |
| Performance of the coherent receiver | p. 42 |
| Transmission on a band-limited channel | p. 59 |
| Introduction | p. 59 |
| Intersymbol interference | p. 60 |
| Condition of absence of ISI: Nyquist criterion | p. 63 |
| Expression of the error probability in presence of Nyquist filtering | p. 68 |
| Transmission on fading channels | p. 69 |
| Characterization of a fading channel | p. 69 |
| Transmission on non-frequency-selective slow-fading channels | p. 73 |
| Theoretical limits | p. 83 |
| Information theory | p. 83 |
| Transmission channel | p. 83 |
| An example: the binary symmetric channel | p. 84 |
| Overview of the fundamental coding theorem | p. 86 |
| Geometrical interpretation | p. 87 |
| Random coding | p. 88 |
| Theoretical limits to performance | p. 91 |
| Binary input and real output channel | p. 91 |
| Capacity of a transmission channel | p. 92 |
| Practical limits to performance | p. 96 |
| Gaussian binary input channel | p. 96 |
| Gaussian continuous input channel | p. 97 |
| Some examples of limits | p. 99 |
| Minimum distances required | p. 100 |
| MHD required with 4-PSK modulation | p. 100 |
| MHD required with 8-PSK modulation | p. 102 |
| MHD required with 16-QAM modulation | p. 104 |
| Bibliography | p. 107 |
| Block codes | p. 109 |
| Block codes with binary symbols | p. 110 |
| Generator matrix of a binary block code | p. 110 |
| Dual code and parity check matrix | p. 112 |
| Minimum distance | p. 113 |
| Extended codes and shortened codes | p. 114 |
| Product codes | p. 115 |
| Examples of binary block codes | p. 115 |
| Cyclic codes | p. 120 |
| Block codes with non-binary symbols | p. 130 |
| Reed-Solomon codes | p. 130 |
| Implementing the encoder | p. 132 |
| Decoding and performance of codes with binary symbols | p. 132 |
| Error detection | p. 132 |
| Error correction | p. 134 |
| Decoding and performance of codes with non-binary symbols | p. 143 |
| Hard input decoding of Reed-Solomon codes | p. 143 |
| Peterson's direct method | p. 144 |
| Iterative method | p. 151 |
| Hard input decoding performance of Reed-Solomon codes | p. 159 |
| Bibliography | p. 160 |
| Appendix: Notions about Galois fields and minimal polynomials | p. 161 |
| Convolutional codes and their decoding | p. 167 |
| History | p. 167 |
| Representations of convolutional codes | p. 169 |
| Generic representation of a convolutional encoder | p. 169 |
| Polynomial representation | p. 172 |
| Tree of a code | p. 173 |
| Trellis of a code | p. 173 |
| State machine of a code | p. 176 |
| Code distances and performance | p. 178 |
| Choosing a good code | p. 178 |
| RTZ sequences | p. 178 |
| Transfer function and distance spectrum | p. 180 |
| Performance | p. 183 |
| Decoding convolutional codes | p. 186 |
| Model of the transmission chain and notations | p. 187 |
| The Viterbi algorithm | p. 187 |
| The Maximum A Posteriori algorithm or MAP algorithm | p. 192 |
| Convolutional block codes | p. 192 |
| Trellis termination | p. 193 |
| Puncturing | p. 196 |
| Bibliography | p. 198 |
| Concatenated codes | p. 201 |
| Parallel concatenation and serial concatenation | p. 203 |
| Parallel concatenation and LDPC codes | p. 206 |
| Permutations | p. 208 |
| Turbo crossword | p. 208 |
| Bibliography | p. 211 |
| Convolutional turbo codes | p. 213 |
| The history of turbo codes | p. 213 |
| Multiple concatenation of RSC codes | p. 215 |
| Turbo codes | p. 217 |
| Termination of constituent codes | p. 221 |
| The permutation function | p. 222 |
| Decoding turbo codes | p. 235 |
| Turbo decoding | p. 235 |
| SISO decoding and extrinsic information | p. 238 |
| Practical considerations | p. 245 |
| m-binary turbo codes | p. 249 |
| m-binary RSC encoders | p. 249 |
| m-binary turbo codes | p. 101 |
| Analysis tools | p. 256 |
| Theoretical performance | p. 256 |
| Asymptotic behaviour | p. 256 |
| Convergence | p. 259 |
| Bibliography | p. 266 |
| Turbo product codes | p. 271 |
| History | p. 271 |
| Product codes | p. 271 |
| Hard input decoding of product codes | p. 273 |
| Row-column decoding | p. 273 |
| The Reddy-Robinson algorithm | p. 274 |
| Soft input decoding of product codes | p. 277 |
| The Chase algorithm with weighted input | p. 277 |
| Performance of the Chase-Pyndiah algorithm | p. 280 |
| The Fang-Battail algorithm | p. 280 |
| The Hartmann-Nazarov algorithm | p. 285 |
| Other soft input decoding algorithms | p. 289 |
| Implantation of the Chase-Pyndiah algorithm | p. 291 |
| Bibliography | p. 293 |
| LDPC codes | p. 297 |
| Principle of LDPC codes | p. 297 |
| Parity check code | p. 298 |
| Definition of an LDPC code | p. 301 |
| Encoding | p. 304 |
| Decoding LDPC codes | p. 308 |
| Random construction of LDPC codes | p. 312 |
| Some geometrical constructions of LDPC codes | p. 315 |
| Architecture for decoding LDPC codes for the Gaussian channel | p. 318 |
| Analysis of the complexity | p. 318 |
| Architecture of a generic node processor (GNP) | p. 319 |
| Generic architecture for message propagation | p. 322 |
| Combining parameters of the architecture | p. 325 |
| Example of synthesis of an LDPC decoder architecture | p. 328 |
| Sub-optimal decoding algorithm | p. 330 |
| Influence of quantization | p. 333 |
| State of the art of published LDPC decoder architectures | p. 335 |
| Bibliography | p. 337 |
| Turbo codes and large spectral efficiency transmissions | p. 343 |
| Turbo trellis coded modulation (TTCM) | p. 343 |
| Pragmatic turbo coded modulation | p. 347 |
| Bibliography | p. 357 |
| The turbo principle applied to equalization and detection | p. 359 |
| Turbo equalization | p. 360 |
| Multipath channels and intersymbol interference | p. 360 |
| The equalization function | p. 362 |
| Combining equalization and decoding | p. 366 |
| Principle of turbo equalization | p. 369 |
| MAP turbo equalization | p. 372 |
| MMSE turbo equalization | p. 381 |
| Multi-user turbo detection and its application to CDMA systems | p. 396 |
| Introduction and some notations | p. 396 |
| Multi-user detection | p. 397 |
| Turbo CDMA | p. 403 |
| Conclusions | p. 405 |
| Bibliography | p. 407 |
| Index | p. 413 |
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