## 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 x_{i}={x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}} 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)=x^{3}+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)