Download AKTU B-Tech 7th Sem 2018-2019 NEC 031 Information Theory And Coding Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 7th Semester (Seventh Semester) 2018-2019 NEC 031 Information Theory And Coding Question Paper

Printed Pages: 3 NECOJ]
Paper Id n-nunn Roll No.
B. TECH
(SEM-VII) THEORY EXAMINATION 2018-19
INFORMATION THEORY AND CODING
Time : 3 Hours Min: Marks : 100
Note : Be precise in your answer. In case of numerical problem assume data wherever not
provided
SECTION ? A
l. Attempt all parts of the following questions: 2Xl0=20
(a) What is Entropy? List the properties of Entropy
(b) What is the minimum value of (pi, p2. p3,?...pn) = H(p) as p ranges over the set of n-
dimensional probability vector? Find all p?s that which achieve this minimum.
(c) State Log-sum inequality.
(d) Define typical set and write its properties.
(e) Write the consequences of AEP.
(1?) State Source Coding theorem.
(g) Show that 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 2 H000, with
equality ifand only ifD'? = p..
(b) What do you mean by Binary symmetric channel?
(i) Differentiate between block codes and covolutional codes.
Li) Given the (5, 4) even parity block code. Find the codewords corresponding to ?1 =
(1011) and i2 = (1010) ?
SECTION B
2. Attempt any three parts of the following questions: 3XIO=30
(a) For the systematic (6,3) code with
[1 0 1]
P = 0 1 1 .
1 1 0
Detect and correct the single error that occurred due to noise. Draw its syndrome
calculation circuit. '
(b) Explain soft-decision decoding with example. Also give benefits of soft decoding.
(c) What is channel? Classify channels into different groups. Explain each type brie?y
and also calculate the channel capacity of each type.
(d) Find the (a) binary and (b) ternary Huffman codes for the random variable X with
_123456
probabilities p ?- 5?5?5'2?1'5?2?1) Also calculate L = Epili in each case.

(e) The convoiutional encoder has the following two generator sequences each of length
3( the same as the constraint length K=3):
1) Input-top adder output path
(93?). 9:1),g?1)) = (1, 1,1)
2) Input-bottom adder output path
(932?.g?2).g?2?) = (1.0.1)
The impulse response of either input-output path of the encoder is the same as the
corresponding sequence of connections from the shift register to the pertinent adder,
with a ?1? representing a connection and a '0? representing no connection.
Find the following:-
(i) Draw the encode; diagram
(ii) Top and bottom output sequences for input sequence 100] 1.
(iii) Find the codeword for input message sequence 1001! using transform
domain approach.
SECTION C
Attempt any one part of the following question: 1X10=10
3. (a) What do you mean by relative entropy and mutual information? State the properties of
relative entropy and mutual information.
(b) Given a binary channel shown in the ?gure below:
l. I
(i) Find the channel transition matrix.
(ii) Find Pm) and P(yz) when P(xn)=P(x:)=0.5.
(iii) Calculate H(X), H(Y), H(Y/X), H(X/Y) and I(X; Y).
Attempt any one part of the following question: IXIO=10
4. (a) State and prove Channel coding theorem.
(b) For the (6, 3) Hamming code, the parity check matrix H is given by
1 0 1 1 0 0
H = 0 1 1 0 1 0]
1 1 1 0 0 1
(i) Construct the generator matrix.
(ii) Determine the codeword that begins with I10.