1
GATE ECE 2022
Numerical
+2
-0

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)
+2
-0.6
Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. GATE ECE 2017 Set 2 Communications - Fundamentals of Information Theory Question 14 English The channel is
A
Lossless
B
Noiseless
C
Useless
D
Deterministic
3
GATE ECE 2016 Set 3
Numerical
+2
-0
A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $${\eta \over 2} = 2.5\, \times \,{10^{ - 5}}$$ Watt per Hz. If information at the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit energy $${E_b}$$ (in mJ/bit) necessary is ________________
Your input ____
4
GATE ECE 2016 Set 2
Numerical
+2
-0
A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:
$${x_0}$$ : a " zero " is transmitted
$${x_1}$$ : a " one " is transmitted
$${y_0}$$ : a " zero " is received
$${y_1}$$ : a " one " is received

The following probabilities are given:
$$P({x_0}) = \,{3 \over 4},\,\left( {\,\left. {{y_0}} \right|{x_0}} \right) = \,{1 \over 2},\,\,and\,P\,\,\left( {\,\left. {{y_0}} \right|{x_1}} \right) = \,{1 \over 2}$$.
The information in bits that you obtain when you learn which symbol has been received (while you know that a " zero " has been transmitted) is _____________

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