## Information Theory and Coding - Dec 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)** State properties of information? Explain types of Entropy, also derive expression for entropy.(10 marks)
**1(a)** What is Entropy? What are its types?(4 marks)
**1(b)** What is compression? Compare different type of compression with example?(10 marks)
**1(b)** Compare Lossy and Lossless compression.(4 marks)
**1(c)** Write a note on convolution code.(4 marks)
**1(d)** State Fermat's little theorem and its applications.(4 marks)
**1(e)** Explain cyclic codes.(4 marks)
**2(a)** Explain various error control strategies in brief.(10 marks)
**2(a)** What do you mean by symmetric key cryptography? Explain DES in detail.(10 marks)
**2(b)** Explain the following terms with example:

i) Hamming distance,

ii) Hamming weight,

iii) Syndrome,

iv) Linear code properties,

v) Code rate.(10 marks)
**2(b)** The generator polynomial for a (7, 4) cyclic code is given by G(D)= 1+D+D^{3}. Compute all systematic codewords.(10 marks)
**3(a)** Explain LZW compression algorithm with example.(10 marks)

### solve any one question from Q.3(a)(i) & Q3(a)(ii).

**3(a)(i)** Explain LZW compression technique with example(10 marks)
**3(a)(ii)** What is cyclic code? How it is generated? For a (7,4) cycle code, find out the generator matrix if G(D)=1+D+D^3(10 marks)
**3(b)** State Chinese Remainder theorem. Using it solve for X.

X=1 MOD 2

X=2 MOD3

X=2 MOD 5(10 marks)

### solve any one question from Q.3(b)(i) & Q3(b)(ii).

**3(b)(i)** Explain Huffman encoding techinque. Encode the data pattern "accabbcdaad" using Huffman technique(10 marks)
**3(b)(ii)** Name the source coding techniques used in the following types of files & classify them as lossy or lossles:

.zip

.jpg

.mpg

.bmp

.gif(10 marks)
**4(a)** Consider the symbols {1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,6,6,7}

i) Find efficient fixed length code.

ii) Find Huffman code

iii) Compare 2 codes.(10 marks)

### solve any one question from Q.4(a)(i) & Q4(a)(ii).

**4(a)(i)** 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)
**4(a)(ii)** Explain Golay code in detail with example.(10 marks)
**4(b)** Explain Modular arithmetic with example.(5 marks)

### solve any one question from Q.4(b)(i) & Q4(b)(ii).

**4(b)(i)** Explain convolution code in brief.(10 marks)
**4(b)(ii)** Which of the following (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)
**4(c)** Compare MD5 and SHA-1(5 marks)
**5(a)** Write short note on random number generation and state when is it needed.(10 marks)
**5(a)** Explain Diffie - Hellman algorithm. Which atttac, is it vulnerable to?(10 marks)
**5(b)** Describe Chinese Remainder Theorem and its applications(10 marks)
**5(b)** Explain the idea of Message Digest 5 (MD 5)(5 marks)
**5(c)** Explain speech compression.(5 marks)

### Write a short note any two Q6.(a,b,c,d)

**6(a)** RSA(5 marks)
**6(b)** RLE(5 marks)
**6(c)** Channel Capacity(5 marks)
**6(d)** Data Encryption statndard (DES)(5 marks)