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Redundancy

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A measure of the possible increase in the transmission rate of information by using a statistical dependence between the components of the information processed at the source of information. The redundancy of a stationary source of information in discrete time processing the information generated by a stationary stochastic process \xi_k\,,\ \ \ k = \ldots, -1,0,1, \ldots where\xi_k takes values in some finite set X with N elements, is defined to be 1 - \frac{\bar H(U)}{H_{\mathrm{max}}} where \bar H(U) is the rate of generation of information by the given source U (see Information, rate of generation of) and H_{\mathrm{max}} = \log N is the maximum possible speed of generation of information by a source in discrete time whose components take N different values.

For references, see at Communication channel.

How to Cite This Entry:
Redundancy. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Redundancy&oldid=33951
This article was adapted from an original article by R.L. DobrushinV.V. Prelov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article