## Digital Communication - May 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.

### Answer any **four**:-

**1 (a)** Does the channel bandwidth requirement reduce by a factor of four in QPSK compared to BPSK?(5 marks)
**1 (b)** Does bandwidth restriction limit the use of Hadamard codes? (5 marks)
**1 (c) ** Is it true that convolutional interleaving requires less memory and offers more flexibility? (5 marks)
**1 (d)** What are different parameters which need to be examined before choosing a PCM waveform for a particular application?(5 marks)
**1 (e)** Derive the condition for maximum entropy of a source. How does entropy vary with probability?(5 marks)
**2 (a)** Consider 5 messages given by probabilities 0.5, 0.25, 0.125, 0.0625, 0.0625. Calculate H.

Use the Shanon Fano algorithm to develop efficient code and for that code calculate the average no. of bits/message. Compare with H. Calculate efficiency and redundancy.(8 marks)
**2 (b)** Consider a systematic block code whose parity check equations are:

p_{1} = m_{1} + m_{2} + m_{4}

p_{2}=m_{1} + m_{3} + m_{4}

p_{3}=m_{1} + m_{2} + m_{3}

p_{4}=m_{2} + m_{3} + m_{4}

Where m_{i} is the i^{th} message digits and P_{i} are the i^{th} parity digits.

(i) Find the generator matrix and parity check matrix.

(ii) How many errors can be detected and corrected?

(iii) If the received code word is 10101010,find the syndrome.(12 marks)
**3 (a)** The bit stream d(t) is to be transmitted using DEPSK. If the d(t) is 0010 1001 1010, determine b(t).

Show that after decoding, the d(t) is recovered.

Show that the fourth bit is in error, then fourth and fifth bits, d(t), will also be in error. (10 marks)
**3 (b)** What is M-ary PSK? Explain with constellation diagram.

What is Euclidian distance for M-ary PSK. Draw and explain 8-ary PSK system with constellation.

What is the bandwidth of M-ary PSK? (10 marks)
**4 (a)** Can there be trade off between signal to noise ratio and bandwidth in calculation of channel capacity? Prove the upper limit of C is C_{∞} = 1.44(S/N)?(12 marks)
**4 (b)** For a (7,4) cyclic code, the generator polynomial g(x) = 1 + x + x^{2}. Find the code word if data is, (i) 0011, (ii) 0100.

Show how cyclic code is decoded to get data word.(8 marks)
**5 (a)** Derive an expression for probability of error of a matched filter.(8 marks)
**5 (b)** Generator vectors for a 1/3 convolution encoder are:

g_{1} = (101), g_{2} = (100), g_{3} = (111). Draw

(i) encoder diagram

(ii) trellis diagram

(iii) using trellis find code vector if message vector is (101100)

(iv) using trellis find message vector if third bit of code vector is in error. (12 marks)
**6 (a)** What is the necessity of equalizers in transmission system? Explain any one equalizer. (10 marks)
**6 (b)** What is MSK? Draw and explain MSK transmitter and receiver. How is it different from GMSK?(10 marks)

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

**7 (a)** Eye Pattern and its applications. (7 marks)
**7 (b)** Line code and its characteristics. (7 marks)
**7 (c)** Effect of Intersymbol Interference. (7 marks)
**7 (d)** Block Diagram of Digital Communication System.(7 marks)