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Q#1
Digital Communication
GATE EC 2025
MCQ
+2 marks
-0.66 marks
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 
?
1/3
1
2/3
4/3
Explanation:
M.L. decoder is used, all symbols are equiprobable
Probability of error 
where 
Probability of transmitting 
Probability of receiving 
when was sent
is given by shaded region:
Thus 
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