END SEMESTER EXAMINATION

B.TECH. (ECE) - SEMESTER-VI

SUBJECT: Information Theory and Coding (EC-312)

Time: 3 Hours

Maximum Marks: 60

Instructions:

1. Attempt all questions.
2. Marks are indicated against each question.

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3. Assume missing data, if any, suitably.

1. (a) Define entropy. Derive the expression for entropy when M messages are equiprobable. [5]
2. (b) A discrete memory less source has an alphabet of five symbols with their probabilities for its output as given here: [5]

   Symbol: S₁ S₂ S₃ S₄ S₅

   Probability: 0.4 0.19 0.16 0.15 0.1

   Construct the Huffman code. Calculate the average code word length, entropy and efficiency of the code.

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3. (a) Apply Shannon-Fano coding procedure to the following message ensemble: [5]

   [X] = [x₁ x₂ x₃ x₄ x₅ x₆ x₇]

   [P] = [0.4 0.2 0.12 0.08 0.08 0.08 0.04]

   Find the average length of the code and variance.

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4. (b) Explain the following terms: [5]
   1. Joint Entropy
   2. Conditional Entropy
   3. Mutual Information
5. (a) What is channel capacity? Derive the channel capacity of Binary Symmetric Channel (BSC). [5]

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6. (b) An analog signal band limited to 10 Hz is to be transmitted over an additive white Gaussian noise channel with SNR of 30dB. Find the channel capacity required to transmit the signal with reliability. [5]
7. (a) Define Linear Block Code. Explain Encoding and Decoding of Linear Block Code. [5]
8. (b) Consider a (7,4) Linear block code defined by the generator matrix [5]

   G =

   i) Find all the code words.

   ii) Determine the error correcting capability of the code.

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9. (a) Design an encoder for the (7,4) binary cyclic code generated by g(x)=1+x+x³ and also trace the steps involved in encoding the message vector 1101. [5]
10. (b) What is Convolutional code? Explain with suitable example. [5]
11. Write short notes on: (Any two) [2x5=10]
    1. Turbo Codes
    2. Viterbi Algorithm

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    3. ARQ Protocols