Code No: 45088

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III B.Tech I Semester Regular Examinations,Nov/Dec 2009 DIGITAL COMMUNICATIONS Common to Electronics And Telematics, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. A DMS has an alphabet of eight letters, Xi , i=1,2,3,,8, with probabilities 0.36,0.14,0.13,0.12,0.1,0.09,0.04,0.02.

(a) Use the Huffman encoding procedure to determine a binary code for the source output. (b) Determine the average number of binary digits per source letter.

[16]

or

(c) determine the entropy of the source.

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2. Construct all possible code words for (7, 3) code with generator matrix  1 0 0 1 0 1 1  G = 0 1 0 1 1 1 0  and determine the correctable error patterns and their 0 0 1 0 1 1 1 corresponding syndromes. [16] 3. (a) Assume that 4800 bits/sec random data are sent over a band pass channel by BFSK signalling scheme. Find the transmitted Band Width BT such that the spectral envelope is down atleast 35 dB outside this band? (b) Write the comparisions among ASK, PSK, FSK and DPSK?

[8+8]

4. (a) Explain the circuit in which the step size adjusts with the signal characteristics. (b) Explain slope overload error in detail.

[8+8]

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5. Consider a telegraph source having two symbols, dot and dash. The dot duration is 0.2s.The dash duration is 3 times the dot duration. the probability of the dots occurring is twice that of the dash, and the time between symbols is 0.2s.Calculate the information rate of the telegraph source. [16]

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6. (a) Draw the block diagram of band pass data transmitter system and explain each block? (b) A band pass data transmitter used a PSK signnalling scheme with S1 (t) = −A CosWc t : 0 ≤ t ≤ Tb S2 (t) = A CosWc t : 0 ≤ t ≤ Tb Tb = 0.2 m sec and Wc = 10π/Tb . The carrier amplitude at the receiver input is 5mv and PSD of gaussion noise is 10−1 w/Hz. Assume that an ideal receiver is used. Calculated Avg bit error of the receiver? [8+8]

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7. (a) Prove that xq (nT s) = x (nT s) + q (nT s) Where xq (nT s) = quantised signal x(nTs) = Original signal q(nTs ) = Quantization error for DPCM transmitter. (b) Explain the reconstruction of original from DPCM transmitter.

[8+8]

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8. A convolutional encoder has two shift registers two modulo-2 adders and an output multiplexer. The generator sequences of the encoder are as follows: g(1) =(1,0,1); g(2) =( 1,1, 1). Assuming a 5bit message sequence is transmitted. Using the state diagram find the message sequence when the received sequence is (11,01,00,10,01,10,11,00,00,......) [16]

2

Code No: 45088

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III B.Tech I Semester Regular Examinations,Nov/Dec 2009 DIGITAL COMMUNICATIONS Common to Electronics And Telematics, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. A carrier system multiplexes 36 voice channels based on 8-bit PCM. The cut off frequency is 7 KHz and the signal is sampled at 8 KHz. No additional bits are added for synchronization. Calculate: (a) Duration of each bit (b) Resultant transmission rate (c) Minimum BW required.

[16]

or

2. (a) What is the entropy of X, where X represents the outcome of a single roll of a fair die. (b) consider a BSC with p(x1)=c (a)show that the mutual information I(x;y) is given by I(x;y)=H(y) + plog2 p + (1-p)log (1-p.) [8+8]

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3. A convolutional encoder has two shift registers two modulo-2 adders and an output multiplexer. The generator sequence s of the encoder are as follows: g(1) =(1,1,0); g(2) =( 0,1, 1).Draw the block diagram of the encoder. Find the encoder output produced by the message sequence 1011101. [16]

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4. In a binary PSK scheme for using a correlator receiver, the local carrier waveform is A cos(Wc t + φ) instead of A cosWc t due to poor synchronization. Derive an expression for error probability and compute the increase in error probability when φ=150 . Assume necessary data if required? [16]   0 0 1 1 1 0 1 5. The generator matrix for a linear binary code is G= 0 1 0 0 1 1 1  1 0 0 1 1 1 0

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(a) Express G in systematic [I P] form .

(b) Determine the parity check matrix H for the code. (c) Construct the table of syndromes for the code.

[16]

6. Explain the working of an integrator and dump based signal receiver. Find its output signal to noise ratio. [16] 7. The cutoff value of the input SNR in PCM is defined as the value of (S/N)i for which the value of (S/N)0 is 10 dB above its minimum. (a) Plot Pe Vs N; N = 2,4,6 and 8 3

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(b) Sketch the threshold value of (S/N)i verses N for N = 2,4,6,8. [Assume psk signalling scheme]. 8. Derive the channel capacity theorem for discrete channels.

[8+8] [16]

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III B.Tech I Semester Regular Examinations,Nov/Dec 2009 DIGITAL COMMUNICATIONS Common to Electronics And Telematics, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. A DMS has 5 equally likely symbols

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(a) Construct a Shannon fano code for X, and calculate the efficiency of the code.

(b) Construct Huffman code for X, and calculate the efficiency of the code. [8+8] 2. (a) Explain in detail about componding. (b) Compare PCM and DPCM.

[8+8]

or

3. Explain in detail about various digital modulation schemes?

[16]

Band width of 20mHz M 4. A bone at a data rate of 5 × 107 bits/sec is used to transmitt over RF Band Pass using ASK signallinsg method. The carrier amplitude at the receiver is 4mv and noise PSD is 1015 W/Hz. Find

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(a) Pe for coherent and noncoherent detection. (b) Compare and conclude for above result.

[16]

5. A source emits one of four possible symbols during each signaling interval. The symbols occur with the probabilities. p1=0.4,p2= 0.3,p3= 0.2,p4=0.1.Find the information gained by observing the source emitting each of these symbols. [16]

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6. The polynomial x15 +1 when factored gives x15 +1 = (x4 +x3 +1)(x4 +x3 +x2 +x+1)(x4 +x+1)(x2 +x+1)(x+1) (a) Construct a systematic (15,5)code using the generator polynomial g(x)=(x4 +x3 +x2 +x+1)(x4 +x+1)(x2 +x+1)

(b) What is the minimum distance of the code?

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(c) How many random errors per code word can be corrected?

[16]

7. A convolutional encoder has a single shift register with two stages,(K=3) three modulo-2 adders and an output multiplexer. The generator sequence s of the encoder are as follows. g(1) =( 0,1, 1) ; g(2) =(1, 0,1),g(3) =(1,1,1). Draw the block diagram of the encoder. Draw the code tree for this encoder. [16] 8. Derive: (a)

E {xo2 (t)} E{nq 2 (t)}

=

3 8π 2

 3 fs fx

5

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(b)



s/ Nq



= 0



1+

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3

f s/ fx

6P ef 12 S π 2 fx fl

Where fS1 - sampled interal f1 ,fx → lower & upper cut off frequencies.

[8+8]

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Code No: 45088

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III B.Tech I Semester Regular Examinations,Nov/Dec 2009 DIGITAL COMMUNICATIONS Common to Electronics And Telematics, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

(a) Find the entropy of the source

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1. A memory less source has the alphabet {-5,-3,-1,0,1,3,5} with corresponding probabilities {0.05,0.1,0.1,0.15,0.05,0.25,0.3}.

(b) design a Shannon Fano code that encodes a single level at a time and determine the average bit rate. [8+8]

[16]

or

2. Derive the expression for SNR of PCM system.

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3. Construct the state diagram for the following encoder. Starting with all zero state,trace the path that correspond to the message sequence 1011101. Given convolutional encoer has a single shift register with two stages,(K=3) three modulo-2 adders and an output multiplexer. The generator sequence s of the encoder are as follows. g(1) =(1, 0, 1) ; g(2) =(1, 1, 0),g(3) =(1,1,1). [16] 4. A DMS has an alphabet of eight letters, Xi , i=1,2,3,,8, with probabilities 0.36, 0.14, 0.13, 0.12, 0.1, 0.09, 0.04, 0.02. (a) Determine the average number of binary digits per source letter (b) Determine the entropy of the source.

[16]

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5. A Binary base band is passed through a raised cosine roll-off filter with a 60% rolloff factor and is then modulated onto a carrier. The data rate is 128/K bits/sec. Find: (a) The approximate BW of a resulting FSK signal when the mark frequency is 150 KHz & the space frequency is 210 KHz.

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(b) The absolute BW of a resulting ASK signal.

[8+8]

p 6. The probability density function of the samoled values of an analog signal is shown in figure 1Design:

(a) A N-level uniform quantizer [N ≥ 4]

(b) A N-level minimum squared error non-uniform quantizer[N ≥ 4]?

[16]

7. With a neat block diagram explain non-coherent detection of ASK receiver and hence derive the expression for probability of error. P e = 1/2 exp [−A2 /8N o] ; if A2  No 7

[16]

Code No: 45088

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Figure 1:

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8. Design a (6,2) cyclic code by choosing the generator polynomial. Determine the generator matrix G for this code and find all possible code words. [16]

8