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:
“To succeed in the other trades, capacity must be shown; in the law, concealment of it will do.”
—Mark Twain [Samuel Langhorne Clemens] (18351910)
“What man or woman of common sense now doubts the intellectual capacity of colored people? Who does not know, that with all our efforts as a nation to crush and annihilate the mind of this portion of our race, we have never yet been able to do it.”
—Angelina Grimké (18051879)
“One would never have guessed that the world had such a capacity for genuine grief. The most we can do is exploit our memories of his excellence.”
—John Cheever (19121982)