SRM University 2007 B.Tech Electronics and Communications Engineering Bank of EC306-Information Theory - Question Paper

16.Find the channel capacity for a BSC for p = 0.6 .
17.Explain about channel reliability functions.
18.Calculate the capacity of lowpass channel with a usable bandwidth of three KHz and S/N=103 at the channel output. presume the channel noise to be Gaussian and
white.


PART-B

1. A binary channel has the subsequent noise characteristic,
0 1
0 2/3 1/3
one 1/3 2/3
a) If the input symbols are transmitted with respective probabilities of 3/4 and 1/4.
obtain the entropies and I(X;Y).
b)Find the channel capacity and the corresponding input probabilities.

2.Find the capacity of the channel with the noise matrix as shown beneath.

½ ¼ 0 ¼
0 one 0 0
0 0 one 0
¼ 0 ¼ ½

3.Find the capacity of the subsequent binary channel.
a)p11= p22 = one . b) p11 = p12 = p21= p22 = 1/2.

4.Find the capacity of the binary channel provided beneath.
p11= p12 = 1/2; p21 = 1/4; p22 = 3/4.


5.Determine the capacity of the unsymmetric channel.

1/3 2/3 0
P(Y/X) = 2/3 1/3 0
0 0 1

6.Find the mutual info and channel capacity of the binary unsymmetric
channel shown in fig. provided p(x1) = 0.6, p(x2) = 0.4.



7.Derive the mutual info for noise free channel.

8.Derive Shannon- Hartley legal regulations.

9.Calculate the bandwidth of the video signal in a TV.
The subsequent are the available data.
1) the no/.of distinguishable brightness levels=10.
2) the no/. of elements per picture frame=300,000.
3)picture frames transmitted per second=30
4)S/N required=30 db.

10. An ideal communication system with avg. power limitation and perturbed by white Gaussian noise has a bandwidth of one MHz and a signal to noise
ratio of 10.
a) Determine the channel capacity in bits per sec.
b) If the signal to noise ratio drops to 5, what bandwidth is needed for the
identical channel capacity.
c) If the band width is reduced to 0.5 MHz,what S/N ratio is needed to
maintain the identical channel capacity.

11.A Gaussian channel has 1MHz bandwidth. compute the channel capacity if the signal power to noise spectral density ratio (s /? ) is 105 Hz . Also obtain the
maximum info rate.






UNIT-V
BLOCK AND CONVOLUTIONAL CODES

PART-A

1. describe systematic code and provide an example.
2. describe nonsystematic code and provide an example.
3. describe code rate.
4. describe Hamming distance.
5. describe Hamming weight of a binary code.
6. What is an extended code?
7. provide any 2 examples for linear block codes.
8. describe Hamming code.
9. describe minimum distance.
10. Mention any 2 properties of a Hamming code.
11. What is a Hadamard code?
12. describe Golay code.
13. elaborate cyclic codes? State its properties.
14. What is a syndrome?
15. What is block interleaving?
16. Mention any 2 methods to decode a convolutional code.
17. What is a repetition code?
18. State the properties of syndrome.
19. What is a perfect code?
20. provide any 3 examples for cyclic code.
21. describe constraint length of a convolutional code.
22. What is viterbi algorithm?



PART-B

1.Consider a [7,4] linear block code with parity check matrix
1 0 one 1 one 0 0
H = 1 one 0 one 0 one 0
0 one 1 one 0 0 1
a) Construct code words for the [7,4] code.
b) Show that this code is a Hamming code.



2. Consider a systematic (6,3) block code generated by the sub matrix

1 one 0
P = 0 one 1
1 0 1
a) write the Parity check matrix H.
b) Tabulate the code words and their weights.

3. A (7,4) cyclic hamming code is generated by G(p) = p3 + 0 + p +1
a). Draw the encoder diagram.
b).Calculate check bit polynomial c(p) when M = 1100.

4. Develop the encoder and syndrome calculator of a cyclic code for
the generator polynomial g(p) = one + D + D3

5. The parity check matrix H of a (7,4) Hamming code is

1 one 1 0 one 0 0
H = 1 one 0 one 0 one 0
1 0 one 1 0 0 1

a) show that GHT = 0 where G is the generator matrix.
b) Find the code for four bit messge 1101

6. Write short notes on
a) Goley code b) BCH code c) Repetition code

7. obtain the convolutional encoder output produced by the message sequence
10111 with code rate r = ½ and constraint length k = 2.


8.Construct the code tree for the convolutioal encoder as shown in fig.
Trace the path through the tree that corresponds to the message sequence 10111.


9. A convolutioal encoder has a single shift register with 2 two stages
i.e constraint length K = two , 3 modulo-2 adders and an output multiplexer.
The generator sequence of the encoder are
g(1) = ( 1,0,1) , g(2) = ( 1,1,0) , g(3) = ( 1,1,1).
Draw the block diagram of the encoder.


10. Construct a state diagram for the encoder starting with the all zero state.
Trace the path that corresponds to the message sequence 10111.

Earning:   Approval pending.