Fundamentals of Information Theory · Communications · GATE ECE

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition proba...

Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with probabi...

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...

Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover proba...

A discrete memoryless source has an alphabet $$({a_1},\,{a_2},\,{a_3},\,{a_4})\,$$ with corresponding probabilities$$\left( {{1 \over 2}\,\,,{1 \over ...

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 inde...

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of th...

In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no...

An analog signal is band-limited to 4kHz. sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to...

Consider a binary memoryless channel characterized by the transition probability diagram shown in the figure. The channel is...

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events: $${x_0}$$ : a " ze...

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 \o...

Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right\}$$ and respective probabilit...

Consider the Z- channel given in the figure. The input is 0 or 1 with equal probability. If the output is 0, the probability that the input is also 0...

The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + {P \over {{\sigma ^2}\,W}}} \r...

A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this first 'Head'. The entropy H (L) ...

A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${{C_1}}$$ . If the SNR is doubl...

A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n

A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols,...

A video transmission system transmits 625 picture frames per second. Each frame consists of a $$400\,\, \times \,\,400$$ pixel grid with 64 intensity ...

A binary source has symbol probabilities 0.8 and 0.2. If extension coding (blocks of 4 symbols) is used, the lower and upper bounds on the average cod...

An image uses $$512\, \times \,512$$ picture elements. Each of the picture elements can take any of the 8 distinguishable intersity levels. The maximu...

A source produces 4 symbols with probabilities $${1 \over 2},\,{1 \over 4},\,{1 \over 8}\,\,and\,\,{1 \over 8}.$$ For this source, a practical coding ...