## The Theory of Information and CodingThis revised edition of McEliece's classic is a self-contained introduction to all basic results in the theory of information and coding. This theory was developed to deal with the fundamental problem of communication, that of reproducing at one point, either exactly or approximately, a message selected at another point. There is a short and elementary overview introducing the reader to the concept of coding. Following the main results, the channel and source coding theorems is a study of specific coding schemes which can be used for channel and source coding. This volume can be used either for self-study, or for a graduate/undergraduate level course at university. It includes dozens of worked examples and several hundred problems for solution. |

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### Contents

Entropy and mutual information | 17 |

Discrete memoryless channels and their capacitycost | 50 |

Discrete memoryless sources and their ratedistortion | 75 |

The Gaussian channel and source | 95 |

The sourcechannel coding theorem | 112 |

Survey of advanced topics for part one | 123 |

Linear codes | 139 |

Cyclic codes | 167 |

BCH ReedSolomon and related codes | 230 |

Convolutional codes | 293 |

Variablelength source coding | 330 |

Survey of advanced topics for Part two | 347 |

Appendices | 366 |

384 | |

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Abramson alphabet assume BCH codes bit error probability block codes burst-error burst-error-correcting bursts of length C„_i called capable of correcting Chapter circuit Cmax code of length code's codeword columns components compute convex convolutional code Corollary corresponding coset cyclic code cyclic shift decoding algorithm decoding rule defined definition denote diagram dimensional discrete memoryless entropy erasures error pattern Euclid's algorithm Figure finite Gaussian channel given Golay code Hamming code Hamming distance Hence inequality input integer Jensen's inequality label Lemma linear code Markov chain matrix H minimum distance mod g(x nonzero output pair parity-check matrix path polynomial g(x possible prefix code primitive polynomial Prob problem proof prove quantization random variables random vectors real numbers result satisfying Section Show source coding theorem source symbol subset syndrome test channel Theorem 2.4 theory ticks transition probabilities transmitted vertex weight enumerator