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. 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.

                                                                            12-4-13

Name:Torrechiva Lester C Year&section:Grade 8- Sardonyx Teacher:Mrs:Villaran

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                 title->Tunay na kaibigan 

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  Ako ay may kaibigan ito ay si ruben jundarino
sya ay kababata ko at lagi kong lasama kahit
sa kalokohan jan kame nag kakasundo.

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sya ay masayahing tao

at mapagbigay pati hindi kanya
iiwan sa ere kahit na mag karoon
pa nang gulo.

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Ang kaibigan kong ito ay hindi

nagpapaasa kung may tulong  na
ibibigay sayo handa syang tumulong

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Sya ay pang apat sa mag kakapatid

marami na rin  kaming pinag samahan
gulo,pang huhuli ng isda sa fishpan,
at higit sa lahat pati sa mga love life
namin  kami parin ang mag karamay kaya
sya ang matatawag kong tunay na kaibigan.

References

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