## Information theory and reliable communication |

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### Contents

Preface | 3 |

Finite State Channels | 22 |

Source Coding with a Distortion Measure | 50 |

Copyright | |

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alphabet assume average distortion average mutual information bility binary digits branching process capacity channel coding channel encoder choose code words completely stationary random completing the proof conditional entropy conditional probability assignment convex define denote deterministic function distortion measure ensemble of codes entropy equation error probability exists expected number expected value exponent Figure Finally finite state channels freezing barriers Gallager given inequality infimum information theory initial input and output input probabilities input sequence joint entropy lemma lower bound Markov chain Mn(y noisy channel nonnegative number of particles obtain output sequence particle crossing proba probability measure probability vector Qa(u random variables random walk rmax Rn(D satisfied with equality source coding theorem source output source symbol space stationary random tree statistically independent take the expected tightest bound tion total number transition probabilities transmitted upper bound zero