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| In [[mathematics]], a '''Markov information source''', or simply, a '''Markov source''', is an [[information source (mathematics)|information source]] whose underlying dynamics are given by a stationary finite [[Markov chain]].
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| ==Formal definition==
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| An '''information source''' is a sequence of [[random variable]]s ranging over a finite alphabet Γ, having a [[stationary distribution]].
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| A Markov information source is then a (stationary) Markov chain ''M'', together with a function
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| :<math>f:S\to \Gamma</math>
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| that maps states ''S'' in the Markov chain to letters in the alphabet Γ.
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| A '''unifilar Markov source''' is a Markov source for which the values <math>f(s_k)</math> are distinct whenever each of the states <math>s_k</math> are reachable, in one step, from a common prior state. Unifilar sources are notable in that many of their properties are far more easily analyzed, as compared to the general case.
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| ==Applications==
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| Markov sources are commonly used in [[communication theory]], as a model of a [[transmitter]]. Markov sources also occur in [[natural language processing]], where they are used to represent hidden meaning in a text. Given the output of a Markov source, whose underlying Markov chain is unknown, the task of solving for the underlying chain is undertaken by the techniques of [[hidden Markov model]]s, such as the [[Viterbi algorithm]].
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| ==See also==
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| *[[Entropy rate]]
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| ==References==
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| *Robert B. Ash, ''Information Theory'', (1965) Dover Publications. ISBN 0-486-66521-6
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| {{probability-stub}}
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| [[Category:Probability theory]]
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| [[Category:Stochastic processes]]
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| [[Category:Statistical natural language processing]]
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Latest revision as of 22:12, 5 May 2014
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