1
GATE ECE 2008
+2
-0.6
Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is
A
$${p^3} + 3{p^2}\left( {1 - p} \right)$$
B
$${p^3}$$
C
$${\left( {1 - p} \right)^3}$$
D
$${p^3} + {p^2}\left( {1 - p} \right)$$
2
GATE ECE 2007
+2
-0.6
During transmission over a certain binary communication channel, bit errors occurs independently with probability p. The probability of at most one bit in error in a block of n bits is given by
A
$${p^n}$$
B
$$1 - {p^n}$$
C
$$np{\left( {1 - p} \right)^{n - 1}} + {\left( {1 - p} \right)^n}$$
D
$$1 - {\left( {1 - p} \right)^n}$$
3
GATE ECE 2007
+2
-0.6
An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’. The values of a and b are

A
a = 1/6 and b = 1/12
B
a = 1/5 and b = 3/40
C
a = 1/4 and b = 1/16
D
a = 1/3 and b = 1/24
4
GATE ECE 2007
+2
-0.6
An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’. Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is

A
$${152 \over 9}$$
B
$${64 \over 3}$$
C
$${76 \over 3}$$
D
$$28$$
GATE ECE Subjects
Network Theory
Control Systems
Electronic Devices and VLSI
Analog Circuits
Digital Circuits
Microprocessors
Signals and Systems
Communications
Electromagnetics
General Aptitude
Engineering Mathematics
EXAM MAP
Joint Entrance Examination