1
GATE ECE 2024
+2
-1.33

The information bit sequence {1 1 1 0 1 0 1 0 1} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is ____.

A

{1 1 1 0 1 0 1 1 1 0 0}

B

{1 1 1 0 1 0 1 1 1 0 1}

C

{1 1 1 0 1 0 1 1 1 1 0}

D

{1 1 1 0 1 0 1 0 1 0 0}

2
GATE ECE 2022
Numerical
+2
-0

Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for y given xA and xB are :

$${f_{\left. Y \right|{x_A}}}(y) = {e^{ - (y + 1)}}u(y + 1)$$,

$${f_{\left. Y \right|{x_B}}}(y) = {e^{(y - 1)}}(1 - u(y - 1))$$,

where, u( . ) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).

3
GATE ECE 2017 Set 1
+2
-0.6
In binary frequency shift keying (FSK), the given signal wave forms are
$$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and
$${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$

where T is the bit-duration interval and t is in seconds. Both $${u_o}(t)$$ and $${u_1}(t)$$ are zero output the interval $$0 \le \,\,t\, \le \,T$$. With a matched filter (correlator ) based receiver, the smallest positive value of T (in milliseconds) required to have $${u_o}(t)$$ and $${u_1}(t)$$ uncorrelated is

A
0.25 ms
B
0.5 ms
C
0.75 ms
D
1.0 ms
4
GATE ECE 2016 Set 2
Numerical
+2
-0
An ideal band-pass channel 500Hz-2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is____________________