Information source (mathematics)

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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\{\bold{X}\} = \lim_{n\to\infty} 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\{\bold{X}\} = \lim_{n\to\infty} 
\frac{H(X_0, X_1, \dots, X_{n-1}, X_n)}{n+1}.

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