Information, transmission rate of

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A quantity characterizing the amount of information that is contained in the output signal of a communication channel relative to the input signal, calculated in a unit of time (cf. Information, amount of). If

are stochastic processes in discrete or continuous time, being the input and output signals of a communication channel, then the quantity


is the transmission rate of information (if the limit exists). Here is the amount of information, is the segment of and is analogously defined. The existence of the limit in (*) has been proved for the large class of channels in which the signals and are stationary and stationarily-related stochastic processes. An explicit computation of the transmission rate of information is possible, in particular, for a memoryless channel and a Gaussian channel. E.g., for a Gaussian channel, whose signals and are Gaussian stationary processes forming a joint Gaussian stationary pair of processes, the transmission rate of information is given by

where and are the spectral densities of and , respectively, and is their joint spectral density.


[1] R. Gallagher, "Information theory and reliable communication" , Wiley (1968)
[2] M.S. Pinsker, "Information and informational stability of random variables and processes" , Holden-Day (1964) (Translated from Russian)
How to Cite This Entry:
Information, transmission rate of. Encyclopedia of Mathematics. URL:,_transmission_rate_of&oldid=13228
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