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

$H\{\mathbf {X} \}=\lim _{n\to \infty }H(X_{n}|X_{0},X_{1},\dots ,X_{n-1})$

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

$H\{\mathbf {X} \}=\lim _{n\to \infty }{\frac {H(X_{0},X_{1},\dots ,X_{n-1},X_{n})}{n+1}}.$

See also

• Markov information source
• Asymptotic equipartition property

References

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