Markov source A discrete memoryless source generates successive messages (symbols) randomly, independently of the source history. Such source probabilistic description is dependent of a time origin and is called non-stationary. A discrete source is defined to be stationary, if its probabilistic description is independent of a time origin. A stationary source can be approximated by a source with memory, the so called Markov source.
Markov source of the L -the order is a source that generates M messages (symbols) described by probabilities and conditional probabilities , where , is a sequence emitted prior to .
Such sequence is called state of Markov source . Thus, it can be viewed that Markov source ( source with memory ) is characterized by a set of states: . The state can be thought of as representing the effect of the source history of on the actually generated message . The state could be the previous symbol from the source or it could be the previous L symbols. For the given stationary source, it is possible to model as much memory as required.
Entropy of the Markov source:
where,
As examples, binary source of the 1 st and of the 2 nd order are considered.
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