{{short description |Sequence of random variables}} {{Inline|date=September 2020}} {{one source |date=March 2024}} 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== An '''information source''' is a sequence of random variables ranging over a finite alphabet <math>\Gamma</math>, having a stationary distribution.
A Markov information source is then a (stationary) Markov chain <math>M</math>, together with a function
:<math>f:S\to \Gamma</math>
that maps states <math>S</math> in the Markov chain to letters in the alphabet <math>\Gamma</math>.
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.
==Applications== 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== *Entropy rate
==References== *Robert B. Ash, ''Information Theory'', (1965) Dover Publications. {{isbn|0-486-66521-6}}
Category:Markov processes Category:Statistical natural language processing
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