# Markov information source

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 Γ, having a stationary distribution.

A Markov information source is then a (stationary) Markov chain *M*, together with a function

that maps states *S* in the Markov chain to letters in the alphabet Γ.

A **unifilar Markov source** is a Markov source for which the values are distinct whenever each of the states 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

## References

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