1

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

$${x_0}$$ : 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 _____________

Your input ____

2

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 ____

3

GATE ECE 2016 Set 1

Numerical

+2

-0

Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right\}$$ and respective probabilities of occurrence $$P = \left\{ {{1 \over 2},\,{1 \over 4},\,{1 \over 8},\,{1 \over {16}},\,{1 \over {32}},......} \right\}$$. The entropy of the source (in bits) is__________.

Your input ____

4

GATE ECE 2014 Set 4

Numerical

+2

-0

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 equals____________________________________

Your input ____

Questions Asked from Fundamentals of Information Theory (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE ECE Subjects

Signals and Systems

Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform

Network Theory

Control Systems

Digital Circuits

General Aptitude

Electronic Devices and VLSI

Analog Circuits

Engineering Mathematics

Microprocessors

Communications

Electromagnetics