## Modern Coding TheoryHaving trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system? This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager's original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor's solutions and figures, available online: www.cambridge.org/9780521852296. |

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Very informative

I recommend it for anyone doing a research or a project on ldpc or turbo codes. . It is really helpful

### Contents

LXXI | 294 |

LXXII | 297 |

LXXIII | 303 |

LXXIV | 308 |

LXXV | 312 |

LXXVI | 314 |

LXXVII | 316 |

LXXVIII | 323 |

XI | 27 |

XII | 32 |

XIII | 35 |

XIV | 44 |

XV | 49 |

XVI | 50 |

XVII | 51 |

XVIII | 54 |

XIX | 57 |

XX | 64 |

XXI | 65 |

XXIII | 67 |

XXIV | 68 |

XXV | 71 |

XXVII | 72 |

XXVIII | 75 |

XXIX | 76 |

XXX | 82 |

XXXI | 83 |

XXXII | 87 |

XXXIII | 94 |

XXXIV | 95 |

XXXV | 96 |

XXXVI | 97 |

XXXVII | 98 |

XXXVIII | 100 |

XXXIX | 101 |

XL | 108 |

XLI | 111 |

XLII | 113 |

XLIII | 114 |

XLIV | 115 |

XLV | 122 |

XLVI | 131 |

XLVII | 134 |

XLVIII | 143 |

XLIX | 148 |

L | 156 |

LI | 160 |

LII | 169 |

LIII | 175 |

LIV | 209 |

LV | 214 |

LVI | 216 |

LVII | 217 |

LVIII | 221 |

LIX | 226 |

LXI | 230 |

LXII | 234 |

LXIII | 245 |

LXIV | 249 |

LXV | 257 |

LXVI | 258 |

LXVII | 261 |

LXVIII | 267 |

LXIX | 283 |

LXX | 291 |

LXXIX | 334 |

LXXX | 336 |

LXXXI | 339 |

LXXXII | 341 |

LXXXIII | 344 |

LXXXIV | 346 |

LXXXV | 347 |

LXXXVI | 349 |

LXXXVII | 363 |

LXXXVIII | 365 |

LXXXIX | 369 |

XC | 375 |

XCI | 381 |

XCII | 382 |

XCIII | 389 |

XCIV | 397 |

XCV | 405 |

XCVI | 410 |

XCVII | 418 |

XCVIII | 421 |

C | 427 |

CI | 428 |

CII | 429 |

CIII | 431 |

CIV | 434 |

CV | 435 |

CVII | 437 |

CVIII | 443 |

CIX | 448 |

CX | 452 |

CXI | 456 |

CXIII | 457 |

CXIV | 459 |

CXV | 460 |

CXVII | 462 |

CXVIII | 464 |

CXIX | 477 |

CXXI | 478 |

CXXII | 479 |

CXXIII | 480 |

CXXIV | 482 |

CXXV | 484 |

CXXVI | 490 |

CXXVII | 497 |

CXXVIII | 500 |

CXXIX | 501 |

CXXX | 502 |

CXXXI | 505 |

CXXXII | 506 |

CXXXIII | 507 |

CXXXIV | 529 |

CXXXVI | 530 |

535 | |

CXXXVIII | 537 |

CXXXIX | 551 |

559 | |

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### Common terms and phrases

aBMSC assume asymptotic belief propagation binary erasure channel bipartite graph blocklength BMS channel BP decoder check nodes check-node codewords computation graph Consider converges convolutional codes corresponding curve degree distribution pair dened denition denote density evolution dierent discussed ecient edge elements encoder entropy eorem eory equations erasure channel erasure probability erefore error probability example EXIT function factor graph Figure follows FSFG GEXIT IEEE IEEE Int IEEE Trans input iterative decoding L-density LDPC codes Lemma limsup linear code log-likelihood ratio low-density parity-check codes MAP decoding memoryless messages minimum distance nodes of degree output parameter parity-check matrix performance permutation polynomial Problem Proc proof random variable Section sequence shows strictly positive suciently symmetric Symposium on Inform Tanner graph theorem threshold turbo codes upper bound variable nodes vector weight distribution xed point zero