Channel with a finite memory
A communication channel for which the statistical properties of the output signal at a time are determined by the input signals transmitted at the times , (and therefore do not depend on the signals transmitted prior to the time ); the number is called the size (or length) of the memory of the channel.
More precisely, a discrete-time communication channel where the input and output signals are given, respectively, by random sequences and with values in the spaces and is called a channel with a finite memory if a compatible set of conditional distributions
by means of which such a channel can be defined, satisfies for any , and the conditions
Here , , and (respectively, ) is a set in the direct product of (respectively, ) copies of . A continuous-time channel with a finite memory is defined similarly.
|||A.Ya. Khinchin, "On the basic theorems of information theory" Uspekhi Mat. Nauk , 11 : 1 (1956) pp. 17–75 (In Russian)|
|||A.A. Feinstein, "Foundations of information theory" , McGraw-Hill (1968)|
|||J. Wolfowitz, "Coding theorems of information theory" , Springer (1964)|
Channel with a finite memory. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Channel_with_a_finite_memory&oldid=11735