## An hypothesis testing approach to information theory, by Richard E. Blahut |

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### Contents

List of Illustrations | x |

Preliminaries | 1 |

Minimization of Convex Functions | 19 |

5 other sections not shown

### Common terms and phrases

achieve E(R additive Gaussian noise algorithm alphabet arbitrary block codes channel capacity channel coding Chernoff bound codewords components constraint with equality continuous function defined convex function Corollary decision regions decoder Definition developed discrete discrimination distribution q dxdy entropy equality constraints error exponent function finite fixed following are satisfied following theorem given hence continuous function hypothesis testing problem inequality constraint infimum information theory interval J J J Kuhn-Tucker conditions Kuhn-Tucker theorem l/l+s Lagrange multiplier Lemma Let q lower bound max max maximum memoryless minimization minimum mutual information n-tuple ne(r output probability distributions probability of error probability vector Proof Let proved quadratic constraint random variables rate distortion function rate distortion theory reliability rate function Reliability-Rate Function satisfies the constraint sequence source codes strictly decreasing Suppose theory of Chapter Toeplitz Toeplitz matrix type 2 error upper bound variance vector space XG(F Xg(x zero