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GATE EC 2024 Set 1 — Question 45

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MCQ+2 / -0.67MediumError ProbabilityDigital Modulation & DetectionCommunications

Communications → Digital Modulation & Detection → Error Probability

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A source transmits a symbol ss, taken from {−4,0,4}\{-4, 0, 4\} with equal probability, over an additive white Gaussian noise channel. The received noisy symbol rr is given by r=s+wr = s + w, where the noise ww is zero mean with variance 4 and is independent of ss. Using Q(x)=12π∫x∞e−t22dtQ(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-\frac{t^2}{2}} dt, the optimum symbol error probability is _______.
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