Download AKTU B-Tech 4th Sem 2016-17 Information Theory And Coding Question Paper

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B.TECH.

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THEORY EXAMINATION (SEM–IV) 2016-17

INFORMATION THEORY AND CODING

Time: 3 Hours

Max. Marks : 100

Note: Be precise in your answer. In case of numerical problem assume data wherever not provided.

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SECTION – A

1. Explain the following: 10 x 2 = 20

1. Draw the block diagram of communication system
2. At what condition entropy attains maximum value? Write the expression for source efficiency
3. Out of following code which one is non singular?

   Source	S1	S2	S3	S4
   Code A	00	001	101	110
   Code B	00	100	111	00

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4. List out two important properties of mutual information
5. State Shannon Hartley Theorem with expression.
6. List out the properties of Block codes.
7. Find the hamming weight of two code vectors C1=0001010, C2=1010101
8. What are convolutional codes? How is it different from block codes?

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9. Obtain an Expression for zero memory information sources emitting independent sequence of symbols
10. Why (23, 12) Golay code is called Perfect code?

SECTION – B

Attempt any five of the following questions: 5 x 10 = 50

2. 1. (i) A source emits one of the four possible messages S1, S2, S3 and S4 with probabilities 4/11, 3/11, 2/11 and 2/11 respectively. Find the entropy of the source. List all the elements for the second extension of the source. Hence show that H (S²) =2 H(S).
      

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      (ii) Discuss the properties of Entropy
   2. (i) Discuss External Property of Entropy with examples
      (ii) Explain the need for source coding in communication system and discuss about compact code
   3. (i) Consider the following S={X1, X2, X3, X4, X5, X6} with probability P= {0.4, 0.2, 0.2, 0.1, 0.08, 0.02}.Find the code words using Shannon fano Algorithm and efficiency of source
      (ii) Clearly explain differential entropy of continuous signal. How it is different from entropy of discrete signals?

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   4. (i) Explain the properties of Mutual information.
      (ii) For a Systematic (7, 4) linear block code, the parity matrix P is given by
      P =

       1 1 1 1 1 0 1 0 1 0 1 1 

      (A) Find all possible code vectors.
   5. (i) Discuss the data compression techniques
      (ii) Consider the (4,3,2)code with input sequence u¹=(101), u²=(110) and u³=(011). The corresponding input polynomials are u(¹)(D)= 1+D2, u(2)(D)=1+D. construct the codeword using transform domain approach.

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   6. (i) A transmitter has symbol consisting of five letters {a1, a2, a3, a4, a5} and receiver as a symbol of four letters {b1, b2, b3, b4}.The joint probabilities of the system are given as
      P (A, B) =

       0.25 0 0 0 0.10 0.30 0 0 0 0.05 0.10 0 0 0.05 0.1 0 0 0.05 0 0 

      Compute H (A), ? (?), ? (A, B) and I(A,B).
   7. (i) Discuss about (i) priori entropy (ii) Posteriori Entropy (iii) Equivocation
      (ii) Explain uniquely decodable code and optimal code.
   8. (ii) An information source produces sequences of independent symbols having the following probabilities. Construct ternary code using Huffman coding procedure and find it efficiency.

      A	B	C	D	E	F	G
      1/3	1/27	1/3	1/9	1/9	1/27	1/27

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   9. (i) Explain the Concept of Shortened Cyclic codes and Burst error correcting codes
      (ii) A source produces sequence of symbols having the following probabilities.

      A	B	C	D	E
      0.25	0.25	0.2	0.15	0.15

      Construct binary code using Shannon fano Elias coding procedure and find its Length and efficiency.

SECTION – C

Attempt any two of the following questions: 2 x 15 = 30

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3. (a) A Binary Symmetric Channel has following matrix with Source probabilities P(X1) = 2/3, P(X2) =1/3. Determine H(X), H(Y), H(Y/X) and Chanel capacity

    3/4 1/4 1/4 3/4 

   (b) Consider the four codes listed below. Identify the instantaneous codes using Kraft Mcmilan inequality theorem

   Source symbol	Code A	Code B	Code C	Code D
   S1	0	0	0	0
   S2	100	10	100	10
   S3	110	110	110	110
   S4	111	11	11	111

4. (a) Write a Short note On:
   1. BCH codes and RS codes
   2. Golay codes
   3. Burst and Random Error correcting codes
   (b) A (6,3) Linear block code has following check bit C4=d1+d2, C5=d1+d3, C6=d2+d3 Construct standard array and decode the received vectwwhs Fit firstranker.com error R=[1011100]

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5. (a) Discuss about hamming distance and minimum distance with good examples.
   (b) Consider the (3,1,2) convolution codes with g(1)=(110), g(2)=(101) and g(3)=(111)
   1. Draw the encoder diagram and find the generator matrix
   2. Find the codeword corresponding to the information sequence (11101) using time domain approach.

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