# 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 ${\displaystyle \Gamma }$, 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

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.