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

R (D) = log (?/D) (0=D= ? )
0 (D> ? )
a) How many bits per sample are needed to represent the outputs of this source with an avg. distortion not exceeding ½ ? ?
b) Plot R (D) for 3 various values of ? and explain the effect of modifications in ? on these plots.


10. It can be shown that if X is a zero-mean continuous random variable with variance ?2 , its rate – distortion function, subject to squared fault distortion measure, satisfies the lower and upper bounds provided by the inequalities
H(X)- ½log two ? eD=R (D) =½log ½ ?2
Where H(X) denotes the differential entropy of the random variable X. Show that for a Gaussian random variable the lower and upper bounds coincide.


11. Consider a DMS with output bits (0, 1) that are equiprobable. describe the distortion measure as D=Pe, where Pe is the probability of fault in transmitting the binary symbols to the user over a BSC.Then the rate - distortion function is
R (D) =1+D log2 D+ (1-D) log2 (1-D), 0=D= Pe =1/2
Plot R (D) for 0=D=1/2


12. Write short notes on upper bound and lower bound on Rate of distortion.

13. discuss scalar Quantization in detail.

14. Explain vector Quantization in detail.

15. Explain the block diagram of a waveform synthesizer for a linear predictive coding.


UNIT-IV

PART-A

1. What is discrete memoryless channel(DMC).
2. What is symmetric channel and draw the structure of it.
3. Derive the channel capacity of symmetric channel.
4. describe independent input and output channel.
5. Draw the structure of BSC and write down the expression of channel matrix.
6. Derive the channel capacity of BSC.
7. What is Binary Erasure channel and draw it.
8. Draw the binary channel with unsymmetric structure and write down the
expression for channel capacity.
9. What is discrete input continuous output channel.
10.Define channel capacity.
11.Define redundancy of the channel.
12.Derive the capacity of noise free channel.
13.State noisy coding theorem.
14.Writedown the expression for Shannon –Hartley legal regulations.
15.Find the channel capacity for a BSC for p = 0.9 .

Earning:   Approval pending.