Z-channel (information Theory) - Capacity

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:

    That way of life against which my generation rebelled had given us grim courage, fortitude, self-discipline, a sense of individual responsibility, and a capacity for relentless hard work.
    Rose Wilder Lane (1886–1968)

    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 (1912–1982)

    Children’s view of the world and their capacity to understand keep expanding as they mature, and they need to ask the same questions over and over, fitting the information into their new level of understanding.
    Joanna Cole (20th century)