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GATE ECE

Fundamentals of Information Theory

Communications

Previous Years Questions

Marks 1

More
Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is r...
GATE ECE 2022
The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in th...
GATE ECE 2022
Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_...
GATE ECE 2017 Set 1
Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetri...
GATE ECE 2017 Set 2
A discrete memoryless source has an alphabet $$({a_1},\,{a_2},\,{a_3},\,{a_4})\,$$ with corresponding probabilities$$\le...
GATE ECE 2016 Set 2
An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four m...
GATE ECE 2016 Set 3
In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 7...
GATE ECE 2012
A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder i...
GATE ECE 2012
An analog signal is band-limited to 4kHz. sampled at the Nyquist rate and the samples are quantized into 4 levels. The q...
GATE ECE 2011

Marks 2

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Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The chann...
GATE ECE 2017 Set 2
A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the followin...
GATE ECE 2016 Set 2
A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise powe...
GATE ECE 2016 Set 3
Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right...
GATE ECE 2016 Set 1
A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this fi...
GATE ECE 2014 Set 1
Consider the Z- channel given in the figure. The input is 0 or 1 with equal probability. If the output is 0, the probab...
GATE ECE 2014 Set 4
The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + ...
GATE ECE 2014 Set 2
A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${...
GATE ECE 2009
A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n
GATE ECE 2008
A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming inde...
GATE ECE 2006
A video transmission system transmits 625 picture frames per second. Each frame consists of a $$400\,\, \times \,\,400$$...
GATE ECE 2001
A binary source has symbol probabilities 0.8 and 0.2. If extension coding (blocks of 4 symbols) is used, the lower and u...
GATE ECE 1991
An image uses $$512\, \times \,512$$ picture elements. Each of the picture elements can take any of the 8 distinguishabl...
GATE ECE 1990
A source produces 4 symbols with probabilities $${1 \over 2},\,{1 \over 4},\,{1 \over 8}\,\,and\,\,{1 \over 8}.$$ For th...
GATE ECE 1989

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