GATE EC 2015 Set 1 — Question 62
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Communications → Digital Modulation & Detection → Error Probability
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Question
A source emits bit 0 with probability and bit 1 with probability . The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value . It is given that the conditional density functions of are asThe minimum decision error probability is
Correct answer
(D) 1/6
Solution
The minimum error probability is achieved by the MAP (Maximum A Posteriori) decision rule: decide 1 if , otherwise decide 0.Given and .
Since , we decide 1 for the interval .
.
(since in this range)..
1.For (where both densities are non-zero):
Since , we decide 1 for the interval .
2.For : only is non-zero, so we decide 0.
3.For : only is non-zero, so we decide 1.
Decision regions: and .The total error probability is ..
(since in this range)..
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