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:
“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)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“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)