## Digital Communication - Dec 2013

### Electronics & Telecomm. (Semester 6)

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)** Compare systematic and non systematic codes.(5 marks)
**1 (b)** Distinguish between channel coding and line coding. (5 marks)
**1 (c) ** Explain Shanon Hartley Theorem. (5 marks)
**1 (d)** Derive the condition for maximum entropy of a source. How does entropy vary with probability? (5 marks)
**2 (a)** Explain the working of QPSK system with neat diagram. (10 marks)
**2 (b)** Draw the signal space representation of QAM system. Calculate the Euclidean distance between two symbols. Derive an expression for transmitted signal.(10 marks)
**3 (a)** Explain the working of duo-binary encoder with precoder. What are the drawbacks of duo-binary encoder? Plot the spectrum of duo binary encoder. (10 marks)
**3 (b)** A discrete memory less source S produces the symbol A, B and C with probabilities 0.4, 0.25, and 0.35, respectively.

(i) Can the output of this source be compressed so that the average codeword length is 2 bits? Give reasons for your answer. Device a Huffman code for this source and determine its coding efficiency.

(ii) Device Huffman code for the second order extension of this source and find the average length of the codewords for this code. What is the coding efficiency?(10 marks)
**4 (a)** What is the necessity of equalizers in transmission system? Explain any one equalizer. (10 marks)
**4 (b)** The parity check equations for a (6, 3) systematic code are:

b_{0}= c_{3}=m_{0}+ m_{1}+m_{2}

b_{1} = c_{4}=m_{0}+ m_{1}

b_{3} = c_{5}=m_{0}+m_{2}

Determine the generator matrix, parity check matrix, list all the code vectors of the code, what is error correcting capability of the code? Prepare appropriate decoding table. Decode the following received code words 101100, 010011 and 001100. (10 marks)
**5 (a)** Consider (3, 1, 2) convolution code with

g^{1} = (101), g^{1} = (110), and g^{1} = (011). Draw the Trellis diagram with minimum four stages. Using this diagram, find the codeword for the sequence (110001).(10 marks)
**5 (b)** Derive code transfer function and explain Viterbi Algorithm. (10 marks)
**6 (a)** Derive an expression for probability of error of a matched filter.(10 marks)
**6 (b)** What is band limiting of signal necessary? What are its disadvantages? List the methods to overcome them. (10 marks)

### Write short notes on (**any three**):-

**7 (a)** CRC Codes.(7 marks)
**7 (b)** ISI and ICI and its remedy.(7 marks)
**7 (c)** Lampel- Ziv Coding. (7 marks)
**7 (d)** GMSK with advantages and disadvantages.(7 marks)