Definition
A binary symmetric channel with crossover probability p denoted by, is a channel with binary input and binary output and probability of error p; that is, if X is the transmitted random variable and Y the received variable, then the channel is characterized by the conditional probabilities
- Pr( Y = 0 | X = 0 ) = 1 − p
- Pr( Y = 0 | X = 1) = p
- Pr( Y = 1 | X = 0 ) = p
- Pr( Y = 1 | X = 1 ) = 1 − p
It is assumed that 0 ≤ p ≤ 1/2. If p > 1/2, then the receiver can swap the output (interpret 1 when it sees 0, and vice versa) and obtain an equivalent channel with crossover probability 1 − p ≤ 1/2.
Read more about this topic: Binary Symmetric Channel
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“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)