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

[math]\displaystyle{ H\{\mathbf{X}\} = \lim_{n\to\infty} H(X_n | X_0, X_1, \dots, X_{n-1}) }[/math]

where

[math]\displaystyle{ X_0, X_1, \dots, X_n }[/math]

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

[math]\displaystyle{ H(X_n | X_0, X_1, \dots, X_{n-1}) }[/math]

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

[math]\displaystyle{ H\{\mathbf{X}\} = \lim_{n\to\infty} \frac{H(X_0, X_1, \dots, X_{n-1}, X_n)}{n+1}. }[/math]

See also

• Markov information source
• Asymptotic equipartition property

References

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

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