Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 4th Semester (Fourth Semester) 2016-17 Information Theory And Coding Question Paper
B.TECH.
THEORY EXAMINATION (SEM?IV) 2016-17
INFORMATION THEORY AND CODING
T ime : 3 Hours Max. Marks : 100
Note .' Be precise in your answer. In case ofnumericalproblem assume data wherever not provided.
SECTION ? A
1. Explain the following: 10 x 2 = 20
(a) Draw the block diagram of communication system
(b) At what condition entropy attains maximum value? Write the expression for source
ef?ciency
(c) Out of following code which one is non singular?
Source S1 82 S3 S4
CodeA 00 001 101 110
Code B 00 100 111 00 ((1) List out
two important properties of mutual information
(e) State Shannon Hartley Theorem with expression.
(1) List out the properties of Block codes.
(g) Find the hamming weight of two code vectors C1=0001010, C2=1010101
(h) What are convolutional codes? How is it different from block codes?
(i) Obtain an Expression for zero memory information sources emitting independent
sequence of symbols
(j) Why (23, 12) Golay code is called Perfect code?
SECTION ? B
2. Attempt any ?ve of the following questions: 5 x 10 = 50
(a) (i) A source emits one of the four possible messages SL Sz, 83 and S4 with
probabilities 4/11, 3/11, 2/ 11 and 2/11 respectively. Find the entropy of the
source. List all the elements for the second extension of the source. Hence show
that H (82) =2 H(S).
(ii) Discuss the properties of Entropy
(b) (i) Discuss External Property of Entropy with examples
(ii) Explain the need for source coding in communication system and discuss about
compact code
(c) (i) Consider the following S={X17 X2, X3, X4, X5, X6} with probability P: {0.4,
0.2, 0.2, 0.1, 0.08, 0.02}.Find the code words using Shannon fano Algorithm
and efficiency of source
(ii) Clearly explain differential entropy of continuous signal. How it is different from
entropy of discrete signals?
(d) (i) Explain the properties of Mutual information.
(ii) For a Systematic (7, 4) linear block code, the parity matrix P is given by
1 1 1
1 1 O
P?
l O 1
O l 1
(A) Find all possible code vectors
(B) A single error has occurred in received vector. Detect and correct the
error R=[1011100]
(e) (1) Discuss the data compression techniques
(ii) Consider the (4,3,2)code with input sequence u1=(101), u2=(110) and
u3=(011).The corresponding input polynomials are u(1)(D)= 1+D2, u(2)(D)=1+D.
construct the codeword using transform domain approach.
(1) (i) A transmitter has symbol consisting of five letters {alj a2, a3; a4) a5} and receiver
as a symbol of four letters {b 1) b2, b3, b4}.The joint probabilities of the system
are given as
0.25 0 0 0
0. 1 0 0.30 0 0
P (A? B) Z 0 0.05 0.10 0
0 0 0.05 0.1
0 0 0.05 0
Compute H (A), H (B), H (A, B) and I(A,B).
(ii) Discuss about (i) priori entropy (ii) Posteriori Entropy (iii) Equivocation
(g) (1) Explain uniquely decodable code and optimal code.
(ii) An information source produces sequences of independent symbols having the
following probabilities. Construct ternary code using Huffman coding
procedure and find it efficiency.
A B C D E F G
1/3 1/27 1/3 1/9 1/9 1/27 1/27
(h) (1) Explain the Concept of Shortened Cyclic codes and Burst error correcting codes
(ii) A source produces sequence of symbols having the following probabilities.
A B C D E
0.25 0.25 0.2 0.15 0.15
Construct binary code using Shannon fano Elias coding procedure and find its
Length and efficiency.
SECTION ? C
Attempt any two of the following questions: 2 x 15 = 30
3. (a) A Binary Symmetric Channel has following matrix with Source probabilities P(Xl) =
2/3, P(Xz) =1/3. Determine H(X), H(Y), H(Y/X) and Chanel capacity
3 1
P [ L j = Z Z
X 1 3
Z Z
(b) Consider the four codes listed below. Identify the instantaneous codes using Kraft
Mcmilan inequality theorem
Source symbol Code A Code B Code C Code D
81 0 0 0 0
$2 100 10 100 10
$3 110 110 110 110
S4 111 11 11 111
4 (a) Write a Short note On:
('0)
(i) BCH codes and RS codes (ii) Golay codes
(iii) Burst and Random Error correcting codes
A (6, 3) Linear block code has following check bit C4=d1+d2, C5=d1+d3D C6=d2+d3
5.
(a)
(b)
(1) Write G and H Matrices (ii) construct standard array table
Discuss about hamming distance and minimum distance with good examples.
Consider the (3,1,2) convolution codes with g(1)=(110), g(2)=(101) and g(3)=(111)
(1) Draw the encoder diagram and find the generator matrix
(ii) Find the codeword corresponding to the information sequence (11101) using
time domain approach.
This post was last modified on 29 January 2020