Information, transmission rate of
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
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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
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where and
are the spectral densities of
and
, respectively, and
is their joint spectral density.
References
[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) |
Information, transmission rate of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Information,_transmission_rate_of&oldid=47354