STUPIDSID
1 (a)
A pair of dice are tossed simultaneously in an experiment outcome first dice is recorded as x1 and 2nd dice as x2 If the two event are:
A{x1, x2 such that x1-x2?8}; B{x1, x2 such that x1 > x2 }
Then determine i) Self information of A and B; ii) Entropy of the experiment.
A{x1, x2 such that x1-x2?8}; B{x1, x2 such that x1 > x2 }
Then determine i) Self information of A and B; ii) Entropy of the experiment.
6 M
1 (b)
Consider the state diagram of a Markov source. Determine: i) State probabilities; ii) Entropy of each state; iii) Entropy of sourse.
8 M
1 (c)
Discuss: i) Additive property of entropy; ii) Symmetrical property of entropy.
6 M
2 (a)
Find the minimum number of symbols 'r' in the coding alphabet for devising an instantaneous code such that W={0, 5, 5, 1, 5} device such a code. Where 'W' represent set of code word of length: 1,2,....n.
6 M
2 (b)
Construct a binary code for a source with five symbols S={s1, s2, s3, s4, s5} with respective probabilities P={-3, -2, -2, -15, -15}. Determine code efficiency using Shannon's coding.
8 M
2 (c)
For the given channel matrix, calculate, H(x), H(y) and channel capacity given P(x1)=6 P(x2)=3 and P(x1)=-1 \[ P(y/x) = \begin{bmatrix}
1/2 &1/2 &0 \\ 1/2
&0 &1/2 \\0
& 1/2 &1/2
\end{bmatrix} \]
6 M
3 (a)
Design a quaternary and binary source code for the source shown using Huffman's coding procedure S={s1, s2, s3, s4, s5, s6, s7}; P={-18, -17, -16, -15, -10, -08, -05} also determine code efficiency.
10 M
3 (b)
Determine channel capacity of a binary erasure channel.
10 M
4 (a)
Consider a random variable 'x' wholes PDF is shown in Fig. Q4 (a).
i) Determine the entropy of the source producing this variable.
ii) If the signal is passed through a linear amplifier of gain '8' determine entropy of o/p.
i) Determine the entropy of the source producing this variable.
ii) If the signal is passed through a linear amplifier of gain '8' determine entropy of o/p.
8 M
4 (c)
A CRT terminal is used to enter alphanumeric data in a system. CRT is connected through a telephone with B,W=3kHz and [S/N]0=10dB. Assuming the terminal has 100 characters and data is sent in an independent manner with equal probability:
i) Find average information per character.
ii) Capacity of channel
iii) Data rate.
i) Find average information per character.
ii) Capacity of channel
iii) Data rate.
8 M
5 (a)
Define the terms; i) Burst error; ii) Systematic linear block code: iii) Ealois field; iv) Hamming weight.
4 M
5 (b)
For a systematic (6, 3) linear block code, the parity matrix is \[ [p]= \begin{bmatrix}1 &0 &1 \\0 &1 &1 \\1 &1 &0
\end{bmatrix}. \] Find all possible code vectors and parity check matrix.
6 M
5 (c)
Construct the standard array for example in Fig. Q5(c). Hence determine corrected vector if received vector, z='000011'.
10 M
6 (a)
For a (7,4) cyclic code the received vector Z(x)=0100101 and the generator polynomial is g(x)=1+x+x3, Draw the ksyndrome calculation circuit and correct the single error in the received vector also explain operation of circuit.
10 M
Write short notes on:
7 (a)
Burst-error correcting codes.
5 M
7 (b)
BCH code.
5 M
7 (c)
Golay code.
5 M
7 (d)
Shortened cyclic codes.
5 M
8
For a (2,1,3) convolutional encoder with g(1)=[1101], g(2)=[1011].
a) Draw the convolutional encoder block diagram.
b) Write down the stat transition table.
c) Draw the code tree.
d) Find the encoder o/p produced by message sequence 1101" by traversing through the code tree."
a) Draw the convolutional encoder block diagram.
b) Write down the stat transition table.
c) Draw the code tree.
d) Find the encoder o/p produced by message sequence 1101" by traversing through the code tree."
20 M
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