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)
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