# WBUT Question Papers EC

### Information Theory Coding And Cryptography B Tech 7th Sem 2008

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Time: 3 Hours ]

[ Full Marks : 70

(Multiple Choice Type Questions)

1. Choose correct answer from the given alternatives for any ten of the following :

Q A ( 7, 4 ) Linear Block Code with minimum distance guarantees error detection

…  of                 –                     – –       – –

a)

£4 bits  b) £ 3 bits

None of these.

c)

£ 2 bits .    d)

Gaussian channel is characterised fay a distribution represented by

a)    pi x) «-j==. e-*2/2®2

V2m

* e-x2/202

p(x)

V2w

Plx}*^ e-*2/**2

p(x)»V2io e-*a/V-ao*.

The binaxy Hamming Codes have the property that

a)              (n,fc) = {2m+l,2m-l-m)

b)              ( n, fc) = ( 2 m – 1, 2 m – 1 + m ) ‘

c)               (a,fc) = {2m-l,2m-l-m)

d)              ( n, fc) * (2»n1, 2m1-m)

Which of the following expression is incorrect ? f­a) H(y/x)«ff(x,y)-H(x)

b)    J(x.y)*H(x)-H(y/x)

c)    Hfx.y)*HTx,y) + H|y)

d)   I(x. y)«H(y)-H(y/x).

77804 (10/12 )

l/tt»f-7/KC-703/0e/(09}

v) For GF (2 3). the elementsla the set are a> ., { 1, 2, 4. 5, 6, 7 } . ty c) { 0. 1. 2, 3 }           d)

Entropy represents

a) amount off information b)

c) measure of uncertainty d)

{ a 1. 2, 3. 4, 5, 6 } {0. 1. 2, 3. 4. 5. 6, 7}.

rate of Information probability of message.

 True False.
 a) b)
 to)

Consider the’Code C * { 0000, 0101,   1010, 1111 } for which compute the minimum distance is

a)         1 b)    2

c) 3 d)                           4.

The generator polynomial of a cyclic code is a factor of

a)        Xn + 1 b).   Xtn+1) + 1

c) X(n+2) +1 d)                none of these.

xttQ Consider the parity check matrix H *

r » ( 001.110). Then the syndrome is gftren by

a)  (110)      b) (100)

c)   (111)      d) <101).

77904 (10/12 )

t-7/BC*703/06/(09)                 5

GROUP – B (8hort Answer Type Questions )

Answer any three of the following. . 3 x 5 * 15

Draw the block diagram of a typical message information communication system.                                                 2

Define Forward Error Correction and Automatic Request for Retransmission.                                                        3

What is systematic format of a code word.               2

Explain Source Coding* and Channel Coding’.             3

A code has the parity check matirixH

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

Discuss the scheme of syndrome decoding of BCH Codes.   4

What is the distance of t-error correcting Reed-Solomion Code. 1.

Consider the primitive polynomial p (Z) *Z4 + Z+ 1 over GF ( 2 ). Use this to construct the expansion field GF ( 16).        –      / 3

Let a s 7 be the pilmitive element, the element of GF ( 16) as a power of a and find out the corresponds minimal polynomial.      t 2

What do you mean by Quantum Cryptography ?

Write some application of cryptography in network security. What is Ste&uio&aphy.               •

77804 (10/12)

GROUP – C

‘ (Long Answer Typegnestlom) ‘ ■

Answer any three questions.       3×15 = 45

8. c0 Consider a systematic (8, 4) code whose parity-check equations are u0*ul+u2+u3 V| *U0+ U j + U 2 l>2*Uo + ui + u3 U3 * U0 + U2 + U3

where v 0, v v v 2 and v 3 are message digits and u 0, v l , v 2, u 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 00 0

0 110 100 1,1 1 0 0 10 i d loooi J

c) . . Prove the following :      ,

If C be an ( n, k ) linear code units parity-check matrix H. For each code vector of Hamming weight I, 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 who&e victor sum is the zero vector, there exists a code vector of Hamming weight lisC.                                       3 + 2 = 5

a)                hi a ( .7, 4 ) cyclic code, if the generator pofynomiai g (x) = 1 + x + x3, find the generator matrix and convert it into systematic forp,                                                   3

1^ Find the parity polynomial and show that the polynomial divides Xn + 1. 3

c)               Consider the message vector polynomial u ( x) = 1 +x 2 + x 3 and find the encoding circuit and complete code vector. 4

d)               Now, find the error pattern and coset leaders for code vector v = ( 1001011 ) and received vector r = ( 1011011 ).

b)               State the Channel capacity of a white, band-limited Gaussian channel
Self-information and Channel capacity,

Derive an expression of noisy channel when bandwidth tends to be veiy long.

1. ■ A discrete memoiyless source has five symbols x lt x 2, x 3, x 4 and x 5 with

probabilities of occurrence P { x 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

b)               average code length

c)               code efficiency. –                         5 + 4 + ( 2 + 2 + 2 )

1. Explain with Mock 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 » 233. Compute the public key Y A and Y B.                                              6 + 4 + 5

1. ^ 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 k. .                       5

c)               Construct the ( 15, 7 ) double error correcting BCH code and code word

C (X) * Xs– + X7 + X® + X4 + 1. Determine the outcome of a decoder when

C(X) Incurs the error pattern e (X) * X7 + X3 + 1.

1. Write short notes on the following :

a)               For a valid and correctly received code word,

When C is the code word and His the parity-check paatrix.

b)                       RSAalgo ’ c) Shannon’s theorems (three) in communication.