Information source (mathematics)

Information source (mathematics)

In mathematics, an information source is a sequence of random variables ranging over a finite alphabet Γ, having a stationary distribution.

The uncertainty, or entropy rate, of an information source is defined as

:H{old{X}} = lim_{n oinfty} H(X_n | X_0, X_1, dots, X_{n-1})

where

: X_0, X_1, dots, X_n,

is the sequence of random variables defining the information source, and

:H(X_n | X_0, X_1, dots, X_{n-1})

is the conditional information entropy of the sequence of random variables. Equivalently, one has

:H{old{X}} = lim_{n oinfty} frac{H(X_0, X_1, dots, X_{n-1}, X_n)}{n+1}

ee also

* Markov information source

References

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


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