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Information Theory and Coding : Question Paper May 2015 - Information Technology (Semester 4) | Mumbai University (MU)

## Information Theory and Coding - May 2015

### Information Technology (Semester 4)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

1 (a) State the properties of information? Also derive the expression for entropy. (5 marks)

1 (b) What is Compression? List different Compression algorithm. Why adaptive Huffman coding is used? (4 marks)

1 (c) Explain Asymmetric key cryptography. (5 marks)

1 (d) What are the security goals? Define Cryptography. (3 marks)

1 (e) Describe Fermat's Little Theorem. (3 marks)

2 (a) Given xi={x1, x2, x3, x4, x5, x6} with probabilities as below:
P(xi)={0.3, 0.25, 0.2, 0.06, 0.04, 0.05, 0.06, 0.04}
i) Determine the efficient fixed length code for the source.
ii) Determine the Huffman code for this source.
iii) Compare the two codes and comment.
(10 marks)

2 (b) Explain convolution code in brief. (10 marks)

3 (a) A (7,4) cyclic code has a generator polynomial: g(x)=x3+x+1.
i) Draw the block diagram of encoder.
ii) Find generator and parity check matrices in systematic form.
(10 marks)

3 (b) Explain Chinese Remainder theorem and also Explain the properties of Modular Arithmetic and Congruences. (10 marks)

4 (a) Describe about Discrete probability and logarithms. (10 marks)

4 (b) For a (6,3) linear block code, the coefficient matrix [p] is as follows: $$P=\begin{bmatrix}0 &1 &1 \\1 &0 &1 \\1 &1 &0 \end{bmatrix}$$ The received code words at the receiver are:
i) 0 0 1 1 1 0 ii) 1 1 1 0 1 1
Check whether they are correct or contains some errors.
(10 marks)

5 (a) Explain Diffie-Hellman algorithm. Which attack is it vulnerable to? (10 marks)

5 (b) Explain convolution code in brief. (10 marks)

6 (a) What do you mean by Symmetric key cryptography? Explain DES in detail. (10 marks)

6 (b) Write a short note on: Type of Entropy and LZW compression. (10 marks)

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