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

$f:S\to \Gamma$

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 $f(s_{k})$ are distinct whenever each of the states $s_{k}$ are reachable, in one step, from a common prior state.

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 hidden Markov models, such as the Viterbi algorithm.

References

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