## Information Theory and Coding - May 2014

### 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)** Explain the physical significance of entropy in information theory(2 marks)
**1(b)** What is compression? List different Compression algorithms.(3 marks)
**1(c)** Describe Fermat's Little Theorem.(3 marks)
**1(d)** Find the generator and parity check matrices of a (7,4)cyclic code with generator polynomial g(X) = 1+X+X^{3}(3 marks)
**1(e)** What is random Number Generation and when it is needed.(3 marks)
**1(f)** What are the security goals?Define Cryptography.(3 marks)
**1(g)** Write about Convolution codes.(3 marks)
**2(a)** Name the source coding techniques used in the following types of files and classify them as lossy or lossless

.zip

.jpg

.mpg

.bmp

.gif(10 marks)
**2(b)** Define generator and parity check matrices of a (7,4)linear block code.

Explain how to generate a linear block code using G-matrix.Explain with an example.(10 marks)
**3(a)** Describes about Discrete probability and logarithms.(10 marks)
**3(b)** Given $$x_{i} ={x_{1},x_{2},x_{3},x_{4},x_{5},x_{6}}\$$ probabilities as below:\ltbr\gt$$p(x_{i})={o.3,0.25,0.2,0.12,0.08,0.05}\$$

Make Huffman code.Find efficiency of this code.(10 marks)
**4(a)** what do you mean by Symmetric key cryptography?Explain DES in detail.(10 marks)
**4(b)** A(7,4) cyclic code has a generator polynomial:g(X) =x^{3}+X+1

Draw the block diagram of encoder and syndrome calculator.

Find generator and parity check matrices in systematic form.(10 marks)
**5(a)** Describe with example Modular Arithmetic,Exponentiation and Congruences.(10 marks)
**5(b)** Explain Diffie-Hellman Algorithm.Which attack,is it vulnerable to?(10 marks)
**6(a)** Write short notes on:

Types Of Entropy(5 marks)
**6(b)** Digital Signature(5 marks)
**6(c)** RLE(5 marks)
**6(d)** Prime Number Generation(5 marks)