Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU)) B-Tech 4th Semester (Fourth Semester) 2018-19 REC406 Information Theory And Coding Question Paper
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REC406
Page 1 of 2
Printed Pages:02 Sub Code: REC - 406
Paper Id: 1102529 Roll No.
B TECH
(SEM IV) THEORY EXAMINATION 2018-19
INFORMATION THEORY AND CODING
Time: 3 Hours Total Marks: 70
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
SECTION A
1. Attempt all questions in brief. 2 x 7 = 14
a. Define channel capacity.
b. What is information rate?
c. Relate the amount of information provided and probability of occurrence of
Events.
d. Why we use logarithmic function to measure information?
e. Describe Extension of Discrete memory less source.
f. List out the properties of Entropy.
g. Define source coding theorem
SECTION B
2. Attempt any three of the following: 7 x 3 = 21
a. Calculate mutual information and capacity of binary erasure channel.
b. State and prove properties of a typical set.
c. Explain the preview of the channel coding theorem and the properties of
channel capacity.
d. Prove the expected length L of any instantaneous D-ary code for a random
variable X is greater than or equal to the entropy HD(X); that is, L ? HD(X),
with equality if and only if D
?li
= pi.
e. Explain the physical significance of different Entropies.
SECTION C
3. Attempt any one part of the following: 7 x 1 = 7
a. Prove that for any countably infinite set of code-words that form a prefix code,
the codeword lengths satisfy the extended Kraft inequality,
And show that the (0, 10, 110 and 111) code-words for transmitting four
messages follows the Kraft inequality.
b. Explain Log Sum Inequality and Data-Processing Inequality.
4. Attempt any one part of the following: 7 x 1 = 7
a. For a binary communication system, a ?0? or ?1? is transmitted. Because of
noise on the channel, a ?0? can be received as ?1? and vice-vers a. Let m0 and
m1 represent the events of transmitting ?0? and ?1? respectively. Let r0 and r1
denote the events of receiving ?0? and ?1? respectively. Let p(m 0) = 0.5,
p(r1/m0) = p = 0.1, P(r0/m1) = q = 0.2
i. Find p(r0) and p(r1)
ii. If a ?0? was received what is the probability that ?0? was sent
iii. If a ?1? was received what is the probability that ?1? was sent.
iv. Calculate the probability of error.
v. Calculate the probability that the transmitted symbol is read correctly at the
receiver.
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| 22-May-2019 09:11:09 | 45.115.62.2
FirstRanker.com | 22-May-2019 09:11:09 | 45.115.62.2
REC406
Page 1 of 2
Printed Pages:02 Sub Code: REC - 406
Paper Id: 1102529 Roll No.
B TECH
(SEM IV) THEORY EXAMINATION 2018-19
INFORMATION THEORY AND CODING
Time: 3 Hours Total Marks: 70
Note: 1. Attempt all Sections. If require any missing data; then choose suitably.
SECTION A
1. Attempt all questions in brief. 2 x 7 = 14
a. Define channel capacity.
b. What is information rate?
c. Relate the amount of information provided and probability of occurrence of
Events.
d. Why we use logarithmic function to measure information?
e. Describe Extension of Discrete memory less source.
f. List out the properties of Entropy.
g. Define source coding theorem
SECTION B
2. Attempt any three of the following: 7 x 3 = 21
a. Calculate mutual information and capacity of binary erasure channel.
b. State and prove properties of a typical set.
c. Explain the preview of the channel coding theorem and the properties of
channel capacity.
d. Prove the expected length L of any instantaneous D-ary code for a random
variable X is greater than or equal to the entropy HD(X); that is, L ? HD(X),
with equality if and only if D
?li
= pi.
e. Explain the physical significance of different Entropies.
SECTION C
3. Attempt any one part of the following: 7 x 1 = 7
a. Prove that for any countably infinite set of code-words that form a prefix code,
the codeword lengths satisfy the extended Kraft inequality,
And show that the (0, 10, 110 and 111) code-words for transmitting four
messages follows the Kraft inequality.
b. Explain Log Sum Inequality and Data-Processing Inequality.
4. Attempt any one part of the following: 7 x 1 = 7
a. For a binary communication system, a ?0? or ?1? is transmitted. Because of
noise on the channel, a ?0? can be received as ?1? and vice-vers a. Let m0 and
m1 represent the events of transmitting ?0? and ?1? respectively. Let r0 and r1
denote the events of receiving ?0? and ?1? respectively. Let p(m 0) = 0.5,
p(r1/m0) = p = 0.1, P(r0/m1) = q = 0.2
i. Find p(r0) and p(r1)
ii. If a ?0? was received what is the probability that ?0? was sent
iii. If a ?1? was received what is the probability that ?1? was sent.
iv. Calculate the probability of error.
v. Calculate the probability that the transmitted symbol is read correctly at the
receiver.
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| 22-May-2019 09:11:09 | 45.115.62.2
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REC406
Page 2 of 2
b. DMS has an alphabet of xi ; i=1,2,3,?.,8; with probabilities 0.25, 0.20,
0.15, 0.12, 0.10, 0.08, 0.05, 0.05. Determine the Entropy & Code efficiency &
code redundancy, using Huffman coding procedure.
5. Attempt any one part of the following: 7 x 1 = 7
(a) Using 3 stage shift register & 2 stage Modulo-2 adder with impulse response of
paths (111) and (101), find the convolution code if the given sequence is
10011, also draw the code tree, state transition diagram.
(b) Derive the expression for channel capacity for infinite bandwidth.
6. Attempt any one part of the following: 7 x 1 = 7
(a) Explain Standard Arrays.
(b) For the given generator polynomial g(x) = 1+x+x
3
find the generator matrix G
for a symmetric (7, 4) cyclic code & find the systematic cyclic code for
message bits 1010.
7. Attempt any one part of the following: 7 x 1 = 7
(a) Using 3 stage shift register & 2 stage Modulo-2 adder with impulse response of
paths (111) and (101), draw trellis diagram and if the transmitted code is
00000000 and received code have error on 2
nd
and 6
th
bit due to channel noise,
then detect and correct the errors by using Viterbi decoding of the convolution
code.
(b) How and when Shortened codes are applied?
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This post was last modified on 29 January 2020