## Information Theory and Coding - Dec 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)** Define Chinese Remainder Theorem and its application(5 marks)
**1 (b)** Explain Term Entropy in Information Theory and its significance.(5 marks)
**1 (c)** Describe Fermat's Little Theorem. And its application(5 marks)
**1 (d)** Explain Cyclic Codes.(5 marks)
**2 (a)** Explain Adaptive Huffman encoding techniques. Encode the data pattern "accabbcdaa" using Above technique.(10 marks)
**2 (b)** Compare Symmetric and Asymmetric Cryptography(5 marks)
**2 (c)** Explain various Security Goals.(5 marks)
**3 (a)** Explain convolution code in brief.(10 marks)
**3 (b)** Consider the source probabilities

{0.20, 0.20, 0.15, 0.15, 0.10, 0.10, 0.05, 0.05}

i) Determine the efficient fixed length code for the source.

ii) Determine Huffman code for this source

iii) Compare the two codes and comment.(10 marks)
**4 (a)** Explain DES and give an outline of the algorithm.(10 marks)
**4 (b)** Which of the following g(x) values guarantees that a single bit error is caught? In each case, what is the error that cannot be caught?

i) x+1 ii) x^{3}(10 marks)
**5 (a)** Describe with example Modular Arithmetic, Exponentiation and Congruences.(10 marks)
**5 (b)** Define:-

i) Hamming Weight

ii) Hamming Distance

iii) Syndrome

iv) Linear Code Properties

v) Code Rate(10 marks)

### Write short notes on:

**6 (a)** RSA(5 marks)
**6 (b)** RLE(5 marks)
**6 (c)** Speech Compression(5 marks)
**6 (d)** Random Number Generation(5 marks)