## Information Theory and Coding - May 2016

### 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)** Write a note on convolution code.(4 marks)
**1(b)** State Fermat's little theorem and its applications(4 marks)
**1(c)** Define entropy and explain types of entropy(4 marks)
**1(d)** Explain cyclic codes.(4 marks)
**1(e)** What is compression. List different compression algorithm.(4 marks)
**2(a)** Name the source coding technique used in the following types of files and Classify them as lossy or lossless.

i) .Zip ii) .jpg iii) .mpg iv) .bmp v) .gif(10 marks)
**2(b)** For (7,4) cyclic code, find out the generator matrix if G(D) = 1+D+D^{3}(10 marks)
**3(a)** Explain Diffie-Hellman algorithm. Which attack is it vulnerable to?(10 marks)
**3(b)** Construct Huffman code for the given symbols {x1, x2...x8} with probabilities P(x) = {0.07, 0.08, 0.04, 0.26, 0.14, 0.19, 0.07, 0.25}. Find coding efficiency.(10 marks)
**4(a)** Explain LZW compression with example.(10 marks)
**4(b)** State Chinese Remainder theorem. Using it solve for X.

X=1 MOD 2

X=2 MOD 3

X=2 MOD 5(10 marks)
**5(a)** What do you mean by symmetric key cryptography? Explain DES in detail.(10 marks)
**5(b)** Define

i) Hamming weight

(ii) Hamming Distance

(iii) Syndrome(10 marks)

### Write short notes on

**6(a)** RSA(5 marks)
**6(b)** RLE(5 marks)
**6(c)** Security Goals(5 marks)
**6(d)** Digital Signature(5 marks)