SRM University 2007 B.Tech Electronics and Communications Engineering Bank of EC306-Information Theory - Question Paper

13.a)A stochastic process is defined by X(t)=Asint + Bcost , where A and B are independent random variable with zero mean and equal standard deviation. Show that the process is stationary.
b) discuss the importance of Gaussian process.


UNIT-2
SOURCE CODING

PART-A
1. describe an alphabet.
2. describe self info and provide its unit.
3. describe mutual info
4. A source produces four symbols with probabilities 1/2, 1/2, 1/8, and 1/8. obtain
the info content of every symbol.
5. A binary source emits a block of ‘K’ binary digits in a provided time.
compute the info content of ‘K’ bit block
6.”If a receiver knows the messages being transmitted, the amount of
info carried will be zero”. Justify
7. describe entropy and provide its unit.
8. What is mutual information?
9. describe info rate, and provide its unit.
10. describe joint entropy.
11. describe conditional info and conditional entropy.
12. List the properties of entropy.
13. List the properties of joint entropy.
14. State source encoding theorem
15. State Kraft-Mcmillan inequality
16. elaborate instantaneous codes?
17. elaborate prefix codes?
18. In a binary PCM, If ‘0’ occurs with a probability of 3/8 and ‘1’ occurs with a
probability of 5/8, compute the amount of info conveyed by the source.
19. describe entropy in continuous cases.
20. Prove that I(X1; X2) = I(X1) + I(X2), Where the symbols signify usual meaning.






PART-B
1. a). discuss the mathematical model for info sources.

b). If there are ‘M’ equally likely and independent symbols, then prove that the amount of info carried by every symbol will be I(X) =N bits, where M=2N and N is any integer.

2. describe and discuss the subsequent terms. a)Entropy b)Joint entropy c)conditional entropy d)Information e)Mutual info f)Conditional info.

3.a) A high resolution black and white TV picture consists of about 2x106 picture elements and 16 various brightness levels. Pictures are repeated at the rate of 32 per second. All picture elements are presumed to be independent and all levels have equal likelihood of occurrence. compute the avg. rate of info conveyed by the TV picture source.

Earning:   Approval pending.