DC IPMORANT QUES

1. (a) 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.
(b) Show that H(X, Y) = H(X) + H(Y |X) = H(Y ) + H(X|Y ).

2. A Binary Symmetric channel is shown in figure

Find the rate of information transmission over this channel when p= 0.9, 0.8 and 0.6. Assume that the symbol rate (or bit) is 1000 bits(symbols)/sec.

3. A voice grade channel of the telephone network has a bandwidth of 3.4 kHz
(a) Calculate the channel capacity of the telephone channel for a signal to noise ratio of 30dB.
(b) Calculate the minimum signal to noise ratio required to support information transmission through the telephone channel at the rate of 4800bps.

4. The parity check bits of a (8, 4) block code are generated by
C5=d1 + d2 + d4
C6=d1 + d2 + d3
C7=d1 + d3 + d4
C8=d2 + d3 + d4
Where d1, d2, d3 and d4 are message bits. Find (a) the generator matrix and parity check matrix for this code. (b) the minimum weight of this code.

5. (a) 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). (i) Find the entropy of the source. (ii) design a Shannon Fano code that encodes a single level at a time and determine the average bit rate.
(b) A Discrete Memoryless Source 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.
(i) Use the Huffman encoding procedure to determine a binary code for the source output.
(ii) Determine the average number of binary digits per source letter.
(iii) Determine the entropy of the source.

6. Decode the following sequence using Viterbi algorithm 11 01 11 of a convolution encoder of size (2,1). Draw the Code Trellis Diagram & Metrics diagram. The encoder outputs are : X1= m +m1+m2 X2= m+m2

7. Consider 1/2 convolution encoder. In which two bits at a time are shifted into it and four output bits are generated. The generators are g(1)=(1, 0,1,0) =g(2)=(0, 1, 0,1), g(3)=(1, 1, 1,0), g(4)=(1, 0, 0,1). Draw the block diagram of the encoder. Draw the code tree for this encoder.

8. Consider a (7,4) cyclic code with g(x)=1 + x + x3
(a) Find all code words
(b) If the received sequence is (1 1 1 0 0 1 1) Find the data word sent.

9. A parity-check code has the parity-check matrix


(a) Determine the generator matrix
(b) Find all the code words.
(c) Suppose that the received word is 110110, decode this received word.

10. The generator matrix for a linear binary code is

(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.