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Ece 526: Information Theory And Security. Question Paper

Ece 526: Information Theory And Security.

Course:Bachelor Of Electrical And Electronics Engineering

Institution: Moi University question papers

Exam Year:2012

ECE 526: Information Theory and Security

QUESTION ONE
a. What is information theory? (3mks)
b. What do you know about random variables? (5mks)
c. Consider the (7,4) Hamming code defined by the generator polynomial g(x) = 1+x+x^3. The code word 0111001 is sent over a noisy channel producing the received word 1111001 that has a single error. Determine the syndrome polynomial S(x) for the received word and show that it is identical to the error polynomial e(x). (6mks)

QUESTION TWO
a. Explain what you know about a sample space. (4mks)

b. Discuss about statistical averages. (5mks)

c. A source emits one of four possible symbols during each signalling interval. The symbols occur with the probabilities:
P(0) = 0.4, P(1) = 0.3, P(2) = 0.2 and P(3) = 0.1. Find the amount of information gained by observing the source emitting each of these symbols. (5mks)

QUESTION THREE
a. Explain the entropy of the source of information. (4mks)

b. Discuss the linear predictive coding system. (5mks)

c. A discrete memoryless source has an alphabet of seven symbols whose probabilities of occurrence are as described:
S(0) = 0.2
S(1) = 0.2
S(2) = 0.12
S(3) = 0.12
S(4) = 0.062
S(5) = 0.062
S(6) = 0.062
Compute the Huffman code for this source, moving a "combined" symbol as high as possible. (5mks)

QUESTION FOUR
a. Describe the joint entropy of the channel . (5mks)
b. Discuss what know about the cyclic codes. (5mks)
c. Consider the transition probability diagram of a binary systematic channel discussed in class. The binary symbol 0 and 1 occur with equal probability. Find the probabilities of the binary symbols 0 and 1 appearing at the channel output. (4mks)

QUESTION FIVE
a. What is the Ergodic process? (5mks)
b. Discuss the Huffman's coding algorithm. (5mks)
c. Consider the (7,4) hamming code and write down the generator matrix G and the parity check matrix H of this code. Show that these two matrices satisfy the condition HG^T =0. (4mks)

QUESTION SIX
a. Describe the mutual information of the channel. (4mks)
b. Using an example explain the Lempel-Ziv coding of information. (5mks)
c. Determine the systematic cyclic code generated by the generator word g= 1100111 corresponding to the data word d= 1111001111. (5mks)

QUESTION SEVEN
a. Discuss what you know about the rate distortion function for the memoryless Gausstan source. (5mks)
b. What is a probability distribution function of a channel? (5mks)
c. Consider the following binary sequence: 11011101011100110110111 use the Lempel-Ziv algorithm to encode this sequence. (4mks)

Ece 526: Information Theory And Security. Question Paper

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