A binary source generates symbols ๐ โ {โ1, 1} which are transmitted over a noisy channel. The probability of transmitting ๐ = 1 is 0.5. Input to the threshold detector is ๐
= ๐ + ๐. The probability density function *f *(๐) of the noise ๐ is shown below:
If the detection threshold is zero, then the probability of error (correct to two decimal places) is ________.
Correct Answer
Solution & Step-by-step Explanation
In the range: 0.12 - 0.14
When 1 is transmitted received signal is:
R = 1 + N
Probability of error
[Area of shaded region] = 1/8
When -1 is transmitted, the received signal is:
Probability of error = Area of the shaded region = 1/8
Total probability of error is:
P[E] = P(x = -1)P + P(x = 1) P
When 1 is transmitted received signal is:
R = 1 + N
Probability of error
[Area of shaded region] = 1/8
When -1 is transmitted, the received signal is:
Probability of error = Area of the shaded region = 1/8
Total probability of error is:
P[E] = P(x = -1)P + P(x = 1) P