1

GATE ECE 2015 Set 1

Numerical

+2

-0

The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is _______.

Your input ____

2

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

A source emits bit 0 with probability $${1 \over 3}$$ and bit 1 with probability $${2 \over 3}$$. The emitted bits are
communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as

$${f_{\left. R \right|o}}\,(r) = \left\{ {\matrix{ {{1 \over 4},} & { - \,3\,\, \le \,\,x\,\, \le \,\,1,\,} \cr 0 & {otherwise,} \cr } } \right.and$$

$${f_{R/o}}\,(r) = \left\{ {\matrix{ {{1 \over 6},} & { - \,1\,\, \le \,\,x\,\, \le \,\,5\,,} \cr 0 & {otherwise.} \cr } } \right.$$

$${f_{\left. R \right|o}}\,(r) = \left\{ {\matrix{ {{1 \over 4},} & { - \,3\,\, \le \,\,x\,\, \le \,\,1,\,} \cr 0 & {otherwise,} \cr } } \right.and$$

$${f_{R/o}}\,(r) = \left\{ {\matrix{ {{1 \over 6},} & { - \,1\,\, \le \,\,x\,\, \le \,\,5\,,} \cr 0 & {otherwise.} \cr } } \right.$$

The minimum decision error orobability is

3

GATE ECE 2014 Set 4

MCQ (Single Correct Answer)

+2

-0.6

Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance $${\sigma ^2}$$. The received signal Y is fed to the threshold detector. The output of the threshold detector $${\hat X}$$ is:
$$$\hat X:\left\{ {\matrix{
{ + \,1,} & {Y\, > \tau } \cr
{ - \,1,} & {Y\, \le \,\,\tau .} \cr
} } \right.$$$
To achieve a minimum probability of error $$P\{ \hat X\, \ne \,X\} $$, the threshold $$\tau $$ should be

4

GATE ECE 2014 Set 4

MCQ (Single Correct Answer)

+2

-0.6

Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the trasmitted symbol $$X\, \in \,\{ \, - \,a,\,\, + \,a\} $$ at any instant, the noise sample Z is chosen independently from a Gaussian distribution with mean $$\beta X$$ and unit variance. Assume a threshold detector with zero threshold at the receiver. When $$\beta $$ = 0 the BER was found to be $$Q\,(a) = 1\, \times \,{10^{ - 8}}$$.
$$\left( {Q\,\,(v)\, = {1 \over {\sqrt {2\,\pi } }}\,\int\limits_v^\infty {{e^{ - {u^2}/2}}} } \right.$$ du, and for v > 1,

use $$Q\,(v) \approx \,{e^{ - {v^2}/2}}$$

When $$\beta = - \,0.3,\,$$ the BER is closed to

use $$Q\,(v) \approx \,{e^{ - {v^2}/2}}$$

When $$\beta = - \,0.3,\,$$ the BER is closed to

Questions Asked from Noise In Digital Communication (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE ECE 2016 Set 1 (2)
GATE ECE 2015 Set 2 (1)
GATE ECE 2015 Set 1 (2)
GATE ECE 2014 Set 4 (2)
GATE ECE 2014 Set 2 (1)
GATE ECE 2013 (1)
GATE ECE 2012 (2)
GATE ECE 2011 (2)
GATE ECE 2010 (2)
GATE ECE 2009 (2)
GATE ECE 2008 (1)
GATE ECE 2007 (5)
GATE ECE 2006 (2)
GATE ECE 2005 (3)
GATE ECE 2004 (1)
GATE ECE 2003 (2)
GATE ECE 2001 (1)
GATE ECE 1999 (2)
GATE ECE 1988 (2)
GATE ECE 1987 (1)

GATE ECE Subjects

Network Theory

Control Systems

Electronic Devices and VLSI

Analog Circuits

Digital Circuits

Microprocessors

Signals and Systems

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

Communications

Electromagnetics

General Aptitude