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In mathematics , a Markov information source , or simply, a Markov source , is an information source whose underlying dynamics are given by a stationary finite Markov chain .

Formal definition [ edit ]

An information source is a sequence of random variables ranging over a finite alphabet ${\displaystyle \Gamma }$, having a stationary distribution .

A Markov information source is then a (stationary) Markov chain ${\displaystyle M}$, together with a function

${\displaystyle f:S\to \Gamma }$

that maps states ${\displaystyle S}$ in the Markov chain to letters in the alphabet ${\displaystyle \Gamma }$.

A unifilar Markov source is a Markov source for which the values ${\displaystyle f(s_{k})}$ are distinct whenever each of the states ${\displaystyle s_{k}}$ 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.

Applications [ edit ]

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 models , such as the Viterbi algorithm .

See also [ edit ]

• Entropy rate

References [ edit ]

• Robert B. Ash, Information Theory , (1965) Dover Publications. ISBN   0-486-66521-6

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