# Difference between revisions of "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 | + | 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 $\xi = ( \ldots, \xi_{-1}, \xi_0, \xi_1, \ldots )$ 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|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|Communication channel]]. | |

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## Revision as of 18:14, 19 October 2014

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 $\xi = ( \ldots, \xi_{-1}, \xi_0, \xi_1, \ldots )$ 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=11410