In information theory, the error exponent of a channel code or source code over the block length of the code is the logarithm of the error probability. For example, if the probability of error of a decoder drops as e–nα, where n is the block length, the error exponent is α. Many of the information-theoretic theorems are of asymptotic nature, for example, the channel coding theorem states that for any rate less than the channel capacity, the probability of the error of the channel code can made to go to zero as the block length goes to infinity. In practical situations, there are limitations to the delay of the communication and the block length of the code cannot be taken to go to infinity. Therefore it is important to study how the probability of error drops as the block length go to infinity.
Famous quotes containing the word error:
“There exists a black kingdom which the eyes of man avoid because its landscape fails signally to flatter them. This darkness, which he imagines he can dispense with in describing the light, is error with its unknown characteristics.... Error is certainty’s constant companion. Error is the corollary of evidence. And anything said about truth may equally well be said about error: the delusion will be no greater.”
—Louis Aragon (1897–1982)