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Coding for Discrete Memoryless Sources
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Actually aperiodic arbitrarily asymptotic behaviour auxiliary distribution Auxiliary Lemmas binary sequence Channel capacity closed set closed state set Coder and Decoder components conditional probabilities Consider corresponding course defined disjoint sets distinct codewords divergence emits encoding rate entropy H erroneous decoding Error Exponent error probability finite following theorem given information loss Information Theory invariant p.d. irreducible law of large length sequences limiting behaviour Longo lower bound Markov chain Markov Sources matrix TT memoryless Moreover Neyman-Pearson lemma overall probability Prob probability distribution probability of erroneous probable sequences Proof of Shannon Proposition random variables row of TT samples satisfy the inequality self-information sequence of letters sequences of length Shannon Theorem Source alphabet Source Coder Source output Source sequences Stationary Distribution stationary p.d. stochastic matrix tends th row Theorem 2.5 transmission errors transmission link typical sequences Udine vector waveforms whence wish zero