Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 10

A useful approximation to 1 / 2 (1 - erf x ) for values of x greater than 3 is given by
Using this approximation, consider an on-off binary system that transmits the signal levels 0 and A with equal probability in the presence of gaussian noise. Let the signal amplitude A be K multiplied by the standard deviation of the noise.
( a ) Calculate the net probability of error if K = 10.
( b ) Find the value of K required to give a net error probability of 10 -5.