# Mumbai University Previous year question papers

## Digital Communication and Coding Techniques

N. B.:

Question No.1 is compulsory.

(2) Attempt any four questions out of remaining six question

(3) Assume suitable data if required.

1. (a) Define the following terms :-

(i) Systematic and non-systematic code

(ii) Hamming weight and Hamming distance

(iii) Entropy and redundancy

(iv) Code rate.

(b) Differentiate between (anytwo) :-

(ii) BPSK and BFSK

(iii) Coherent and non-coherent code detection.

2. (a) Explain the central limit theorem for random variables.

(b) A three digit message is transmitted over a noisy channel having a probability of error P(E) = 2/5 per digit. Find out corresponding PDF and CDF. Also find the probability of more than one error.

(c) For a source transmitting two independent messages m1 and m2 having probabilities of P and (I-P) respectively, prove that entropy is maximum when both the messages are equally likely. Also plot the variation of entropy H as a function of probability (P) of one of the messages.

3. (a) Explain any source coding technique to increase average information per bit.

(b) A discrete memorylesssourcehas five symbols x1′ x2′ x3′ x4 and x5 with probabilities 0-4,0’19,0’16,0’15 and 0’15 respectively attached to every symbol.

(1) Construct a shannon.Fanocode for the source and calculate code efficiency.

(2) Repeat same for Huffman code.

(c) State and explain in brief:-

(i) Shannon’s theorem

(ii) Shannon-Hartley theorem.

4. (a) The generator polynomial of a (7,4) cyclic code is x3 + x + 1.

(i) Sketch an encoder for the same

(ii) Construct the generator matrix for a systematic cyclic code and find the code word used for the message. { 1 1 0 1 (LSB) } using the generator matrix.

(iii) Verify the result using division method.

(b) A K = 3, P = % convolutional encoder can be de~cribed by the impulse response of the paths given by g1 = (1, 1, 1), g2 (1,0,1).

(i) Draw the block diagram of the encoder and obtain the output for data { 1 0 0 1 1 (LSB) }

(ii) Sketch the code tree and trace the path cor’responding to the message sequence in (i).

(iii) Draw the trellis diagram for the encoder.

5. (a) What is duo-binary encoding? Explain with the neat block diagram. How the duo-binary encoding reduces the bandwidth requirements.

(b) Why MSK is called ‘Shaped QPSK’ ? Justify with relevant expressions or waveforms. Discuss the merits of MSK over QPSK.

6. (a) Derive the expression for signal to noise ratio of Integrate and Dump receiver filter.

(b) Derive an expression for error probability of Matched filter.

7. (a) Explain with neat block diagram, direct sequence spread spectrum technique. What is processing Gain and Jamming Margin?

(b) Sketch block diagram of FH / MFSK system. With illustrative figures, distinguish between slow frequency hopping and fast frequency hopping. What is chip rate for the two systems?