1
GATE ECE 2022
Numerical
+1
-0.33

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probability (1 $$-$$ $$\in$$), and flipped with probability $$\in$$. For each codeword transmission, the receiver performs minimum Hamming distance decoding, and correctly decodes the message bits if and only if the channel introduces at most one bit error. For $$\in$$ = 0.1, the probability that a transmitted codeword is decoded correctly is __________ (rounded off to two decimal places).

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2
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?
A
GATE ECE 2017 Set 2 Communications - Fundamentals of Information Theory Question 20 English Option 1
B
GATE ECE 2017 Set 2 Communications - Fundamentals of Information Theory Question 20 English Option 2
C
GATE ECE 2017 Set 2 Communications - Fundamentals of Information Theory Question 20 English Option 3
D
GATE ECE 2017 Set 2 Communications - Fundamentals of Information Theory Question 20 English Option 4
3
GATE ECE 2017 Set 1
Numerical
+1
-0
Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_2}$$ has mean 1 and variance 4. The mutual information I $$\left( {{X_1},\,{X_2}} \right)$$ between $${{X_1}}$$ and $${{X_2}}$$ in bits is ________________.
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4
GATE ECE 2016 Set 3
Numerical
+1
-0
An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $${p_1}$$ = $${p_4}$$ = 0.125 and $${p_2}$$ =$${p_3}$$. The information rate (bits/sec) of the message source is ____________________
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