Formal Definition
Let X represent the space of signals that can be transmitted, and Y the space of signals received, during a block of time over the channel. Let
be the conditional distribution function of Y given X. Treating the channel as a known statistic system, is an inherent fixed property of the communications channel (representing the nature of the noise in it). Then the joint distribution
of X and Y is completely determined by the channel and by the choice of
the marginal distribution of signals we choose to send over the channel. The joint distribution can be recovered by using the identity
Under these constraints, next maximize the amount of information, or the message, that one can communicate over the channel. The appropriate measure for this is the mutual information, and this maximum mutual information is called the channel capacity and is given by
Read more about this topic: Channel Capacity
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)