Capacity
The capacity of the Z-channel with the crossover 1 → 0 probability p, when the input random variable X is distributed according to the Bernoulli distribution with probability α for the occurrence of 0, is calculated as follows.
where is the binary entropy function.
The maximum is attained for
yielding the following value of as a function of p
For small p, the capacity is approximated by
as compared to the capacity of the binary symmetric channel with crossover probability p.
Read more about this topic: Z-channel (information Theory)
Famous quotes containing the word capacity:
“Our capacity to retaliate must be, and is, massive in order to deter all forms of aggression.”
—John Foster Dulles (1888–1959)
“For a transitory enchanted moment man must have held his breath in the presence of this continent, compelled into an aesthetic contemplation he neither understood nor desired, face to face for the last time in history with something commensurate to his capacity for wonder.”
—F. Scott Fitzgerald (1896–1940)
“People between twenty and forty are not sympathetic. The child has the capacity to do but it can’t know. It only knows when it is no longer able to do—after forty. Between twenty and forty the will of the child to do gets stronger, more dangerous, but it has not begun to learn to know yet. Since his capacity to do is forced into channels of evil through environment and pressures, man is strong before he is moral. The world’s anguish is caused by people between twenty and forty.”
—William Faulkner (1897–1962)