GATE EC 2025 Set 1 — Question 41
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Communications → Digital Modulation & Detection → Error Probability
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Question
A source transmits symbol that takes values uniformly at random from the set . The receiver obtains , where is a zero-mean Gaussian random variable independent of . The receiver uses the maximum likelihood decoder to estimate the transmitted symbol .Suppose the probability of symbol estimation error is expressed as follows:where denotes the probability that exceeds 1.What is the value of ?
Correct answer
(D) 4/3
Solution
Given symbols are transmitted with equal probability . The received signal is , where .For uniform priors, the Maximum Likelihood (ML) decoder is equivalent to the Minimum Distance decoder. The decision boundaries are located at the midpoints between adjacent symbols:
- Decide if
- Decide if
- Decide if
1.
2. (due to symmetry of zero-mean Gaussian noise)
3.
Substituting these into the expression:Comparing this with the given form , we find .Continue learning with Success Tracker
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