West Bengal Institute of Technology (WBIT) 2008-7th Sem B.Tech Electronics and Communications Engineering Electronics & Comm ( - ) Coding & Information Theory - Question Paper
ENGINEERING & MANAGEMENT EXAMINATIONS, DECEMBER - 2008 INFORMATION THEORY, CODING AND CRYPTOGRAPHY
- ' SEMESTER-7 . " ' ; : -
Time: 3 Hours ] : r t [ Fvill Marks: 70
(Multiple Choice Type Questions)
1. Choose correct answer from the given alternatives for any ten of the following:
, - i. ' . 10 X 1 * 10
Q A ( 7, 4 ) Linear Block Code with minimum distance guarantees error detection
" " of - _ \ -
a) 4 bits b) 3 bits
c) 2 bits d) None of these.
J9 Gaussian channel to characterised by a distribution represented by
a) p (x) * ~j=- e-*2'2**2
S2mt
b) p(x)-.e-*2/2o2
c) pU>f
d) p(*)*V27ca e-*a/V-aoa .
Wi The binary Hamming Codes have the property that
a) { n, k) = ( 2 m + 1, 2m - 1m ) '
b) ( n, fc) * ( 2 m - 1, 2 m - 1 + m ) '
V c) ( n, k ) * (2 m- 1, 2 m 1 -m)
d) ( n, k) f2-h 2mI -m) /
iv) Which of the following expression is incorrect ?
b) Iix,y)*Hlx)-lUy/x}
c) H(x. y)H(*y) + lf*y>
d) Ux,y)*Hty)-Hiy / Kb
l/BC-7/BC-70S/0e/(0}
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v) For GF (2 9), the elements Hi the set are ai . ( L. 2 3. 4, 5, 6, 7 } . . b) c) {0.1.2,3} d) Entropy represents vl) Q amount of Information b) c) measure of uncertainty d) |
.{0, 1,2,3, 4.5.6} {0. 1. 2, 3. 4. 5. 6, 7}. ' % rate of Information probability of message. |
vH)
viii)
100110 011011, when represent modulo-2 addition for binary number, yields
a) 100111 b) liifoi
c) 000001 d) 011010. |......
In a binary system, the coding efficiency increases on probability of occurrence of O, approaches 0*5.
- , ' i
a)
b)
True
False.
A polynomial is called monic if a) odd terms are unity c) leading coefficient is unity
If m 4. then what will be the length of the BCH Code ?
a) 16 b) 15
c) 17 d) none of these.
to)
b)
d)
even terms are unity leading coefficient is zero.
Consider ther Code C * { 0000, 0101. 1010, 1111 } for which compute the minimum distance is
xi)
7dD
a) 1 b) 2
0 3 d) 4.
The generator polynomial of a cyclic code is a factor of
a) Xn +1 b) Xn+ + 1
c) X(n+a) +1 d) none of these.
100 &1 0 00 1 1 10 0 1 1 - 1 0 1 J
and the received vector
xfU) Consider the parity check matrix H m
r * ( 001.110). Then the syndrome is given by
a) (110) b) (100)
0 ( 111) d) ( 101 ).
f-7/EC-703/08/(09) 5
GROUP -B (8liort Answer Type Qnetdona)
. ' . fi.1 ' f"v > St.- . '
Answer any three of the following. 3 x 5 15
Drawthe block diagram of a typical message information communication system. 2
2. a) b)
3. a) b)
4. #
Define Forward Error Correction and Automatic Request for Retransmission. 3
What is systematic format of a code word. 2
ExplainSource Coding1 and'Channel Coding1. 3
A code has the paiitycheck matttx
110 100 0 140 10 L10 100 1
H
Assuming that a vector ( 111011) is received,
Determine whether the received vector is a valid code. 3
If not, determine what is the probable code vector originally transmitted. If yes', conform. > ..........2
W
a)
b) b)
a)
b)
0
Discuss the scheme of syndrome decoding of BCH Codes. 4
What is the distance of t-error correcting Reed-Solomon Code. 1
Consider the primitive polynomial p (Z) * Z4 + Z + 1 over GF( 2 ). Use this to construct the expansion field GF (16). - / 3
6,
Let a = 7 be the primitive element, the element of GF ( 16) as a power of a and find wit the comsids litftiinitif t 2
2
2
What do you mean by Quantum Cryptography ?
Write some application of cryptography in network security. What is Steganography.
' GROUP - C
(Long Answer Type Questions )
Answer any three questions. 3x15 = 45
8. a) Consider a systematic ( 8, 4 ) code whose parity-check equations are Uo*Ul + U2+U e1su0+u1+u2 u2*u0+ui+u3
. Ojtt0.+ U2+Uji
where v 0, v v v 2 and v 3 are inessage digits and v 0, B j , v v 3 are parity-check digits.
Find the generator and parity-check matrix for the code.
Show that minimum distance of the code Is 4. 4+1=5
b) Pesign the syndrome circuit for which the parts-generate matrix is given by 110 1 000
0 110 10 0
G =
1 1 10 0 10
1 0 1 0 0 0 1 J
c) ,Y Prove the following : ,
If Cbean( a, fc) linear code units parity-check matrix H. For each code vector of Hamming weight U these exists I columns of H such that the vector sum of these I columns is equal to the zero vector. Conversely, if there exists I columns of H wfcfcie Victor sum is the zero vector, there exists a code vector of Hamming weight lisC. ; 3 + 2 = 5
a) fti a ( .7, 4 ) cyclic code, if the generator polynomial g (x) = 1 + x + x3, find the generator matrix and convert it into systematic forp. 3
Find the parity polynomial and show that the polynomial divides Xn + 1. 3
c) Consider the message vector polynomial u ( x ) = 1 + x 2 + x3 and find the encoding circuit and complete code vector. 4
d) Now, find the error pattern and coset leaders for code vector v = ( 1001011 ) aiicl received vector r = ( 1011011 ). 5
Self-information and Channel capacity,
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l/8BM-7/*C-703/08/(09) 7 |
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4x2 |
10. a) Explain the terms and their significance : Entropy, Mutual Information and,
b) State the Channel capacity of a white, band-limited Gaussian channel
Derive an expression of noisy channel when bandwidth tends to be very long.
.
\ ' '3 + 4
11. A discrete memoryless source has five symbols x j, x 2, x 3, x 4 and x 5 with
probabilities of occurrence P { x %) * 0-4, P ( x 2 ) * 0*19, P ( x 3 ) = 0-16, P( x4) * 0-15 and P{ x5) * 01.
Construct the Huffman Code and determine
a) entropy
average code length
c) code efficiency. - 5 + 4 +(2 +2+ 2)
12. Explain With block diagram, the secrecy and authentication algorithm Is secured.
Given N * 119 and public key P u * 5, find the private key P r . Also calculate the
ciphertext C. In the Diffic-Hellman key exchange algorithm let the prime number q * 353. and its primitive root a = 3. For A and B select their secret keys X A = 97 and X B m 233. Compute the public key Y A and Y B. 6 + 4 + 5
13. a) Given the polynomial p (X) = X3 + X+1. Construct the field GF ( 2 3) 5
b) Construct a double error-correcting BCH Code over GF ( 2 3) and determine the value of n and fc. . 5
c) Construct the ( 15, 7 ) double error correcting BCH code and code word
C (X) Xs + X7 + X + X* + 1. Determine the outcome of a decoder when
C ( X) incurs the error pattern e (X) * X 7 + X 2 + 1.
5
14. Write short notes on the following :
a} For a valid and correctly received code word,
. -
CHT * 0.
When C is the code word and H is the. parity-check jnatrlx.
5
5
b) RSAalgo
c) Shannon's theorems (three) in communication.
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| Earning: Approval pending. |
