GATE EC 2018 Set 1 — Question 27
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Communications → Digital Modulation & Detection → Error Probability
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Question
A binary source generates symbols which are transmitted over a noisy channel. The probability of transmitting is 0.5. Input to the threshold detector is . The probability density function of the noise is shown below.
If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.
Correct answer
0.12 to 0.14
Solution
Given:
,
Threshold
An error occurs if:
From the given triangular PDF :
For , the slope is . So, .
By symmetry of the PDF, .Rounding to two decimal places, the probability of error is 0.13.
,
Threshold
An error occurs if:
1. is transmitted but is detected.
2. is transmitted but is detected.
From the given triangular PDF :
For , the slope is . So, .
By symmetry of the PDF, .Rounding to two decimal places, the probability of error is 0.13.
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