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

$H\{\mathbf{𝐗}\}=\underset{n\to \mathrm{\infty }}{\lim }H(X_n|X_0,X_1,\dots ,X_{n-1})$

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

$H\{\mathbf{𝐗}\}=\underset{n\to \mathrm{\infty }}{\lim }\frac{H(X_0,X_1,\dots ,X_{n-1},X_n)}{n+1}.$

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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