## The mathematical theory of communication |

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approximation arbitrarily small average power band binary digits binary number bits per second calculated channel capacity chosen coding communication system communication theory conditional entropy conditional probability consider constraints continuous corresponding defined definition digram dimensional discrete channel distribution duration encoding English ensemble of functions entropy power equal equivocation ergodic example fidelity finite number frequency of errors Gaussian Gaussian distribution given graph Hence high probability Hy(x Hy{x independent information source joint entropy letter frequencies letters limited logarithm Markoff process mathematical maximizing maximum entropy meaning measure noise power noiseless number of possible number of symbols obtain output p(xi perturbed pi log pi prob probability measure problem produced random rate of transmission received signal redundancy relative entropy samples semantic Shannon situation space statistical structure stochastic process subset Suppose telegraphy Theorem tion trans transducer transition probabilities transmitted signal uncertainty white noise white thermal noise words zero