Roll No. .A.R0.
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008603
August/September 2022
B.Tech. (ECE) 6th SEMESTER
Information Theory & Coding (ECEL-602)
Time:3Hours] [Max.Marks 75
Instructions
1. t is compulsory to answer all the questions (1.5 marks
each) of Part-A in short.
2. Answer any four questions from Part-B in detail.
3. Diferent sub-parts of a question are to be attempted
adjacent to each other
PART-A
1. (a) What do you mean by channel coding and source
coding. Differentiate them. (1.5)
b) Differentiate between self and mutual information. And
prove that self information is a special case of mutual
information. (1.5)
(c)What is prefix and prefix free code? Explain with the
help of an example. (1.5)
(d) State Shannon-Hartley theorem for channel capacity
and from that derive Shannon's theoretical limit. Hoow
can this limit be increased? (1.5)
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is this statement
(e) "Entropy is measure of uncertainty",
true. Justify your answer. (1.5)
"When a code is irreducible, it is uniquely decipherable,
but the reverse is not true". Justify the statement.
(1.5)
(g) Is it true that any information source has a unique
code attaining the minimum average length? (1.5)
h) What do you mean by symmetric channel. Write down
state transition matrices for symmetric channels. (1.5)
) Differentiate between Bipolar RZ and NRZ line code.
(1.5)
Comment on the main advantages of Lempel Ziv
algorithm over Huffman coding and Shannon Fano
coding (1.5)
PART-B
2. (a)
(a) Consider a binary input, output channel shown below
X1
0.8
Y1
0.2
X2 -
Y2
0.3
X3 0.7
3
Find H(X), H(Y),
H(XIY), H(Y|X) and H(XY). Give
inference of each entropy calculated.
(10)
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between information and entropy
b) Derive a relationship
State and prove the
for sequence of messages.
a
condition for maximum entropy. (5)
source transmits seven messages at the frequency
3. (a) A
of 1 kHz with the probability given below
X2 x3 X4 X5 X6 X7
X1
0.25 0.2 0.2 0.1 0.1 0.1 0.08
Find entropy and information rate of the source,
construct Huffman code for
i) Using two symbols,
above messages, and
(iii) Find coding efficiency and redundancy. (10)
information
b) Draw Deterministic channel and show that
transfer by this channel is equal to the output entropy.
(5)
of a
4. (a) Derive expression for channel capacity
an
between channel
Gaussian channel and plot a graph
bandwidth keeping S/N ratio constant.
capacity verses
(10)
What is coding efficiency and coding
redundancy?
(b)
efficiency
Give their significance. Show that the coding
is maximum when P(0)= P(1). 5)
3 [P.T.O.
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5. (a) Consider 12 bits binary sequence with a long sequence
of ls followed by a single 0 and then a long sequence
of 1s. draw the waveform for this sequence, using thee
following line codes
) Unipolar NRZ code.
(i) Bipolar NRZ.
ii) Bipolar RZ.
(iv) AMI RZ.
(v) Split Phase (Manchester) line code.
(vi) Polar Quaternary NRZ format. (10)
(b) What is the channel capacity of a binary symmetric
channel with error probability 0.01? (5)
6. (a) Compress the following string Using Lempel Ziv
Coding
ABABBAAABBAAAB
Find efficiency of this compressed code with respect
to fixed length 4 bit code. (8)
b)
b) Give comparison of various line codes on the basis of
) Transmission of DC signal.
i) Signaling Rate.
ii) Noise immunity.
(iv) Synchronizing capability.
(v) Bandwidth. (7)
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7. (a) Prove that mutual information of a continuous channel
1.
can never be negative. (8)
b) Explain Binary Erasure Channel and its significance
in coding theory. How is the concept of no decision
output (y) of Binary Erasure channel materialized in
practice? (7)
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