No. of Pages: 2

AP) ABDUL KALAM TECHNOLOGICAL UNIVERSITY
SECOND SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 201 8

Branch: Electronics and Communication Engineering

Stream(s): Telecommunication Engineering

Course Code & Name: 01 EC6518- Information Theo

Answer any twofull questions from each part
Limit answers to the required points.

Max. Marks: 60 Duration: 3 hours

PARTA

a ‘en ೩ source S= 1S, 8,84, SasSes Ses) .Given ‏۔‎ with probabilities
= (0.3,0.3,0.09,0.09,0.09,0.09,0.04] . Construct a bina: (6) P . Construct a binary code
using Shannon —Fano coding procedure. Calculate average length, variance and efficiency.

b. Given 5 = (5,,5,,5,,5,,5,,5,), X= {0,1} and ॥ -12 = 203 ‏راع‎ = { = (५ = ? . Find (3)

minimum value ofP so that instantaneous code exists.

2. a. Possible outcomes of a random variable Y are Y], and )'3. Two different (3) distributions of
this random variable are p(Y) = (1/2, 1/4, 1/4) and q(Y) = (1/3, 1/3, 1/3). Calculate relative
entropies.

b. State and prove the necessary and sufficient condition for the existence of (6) instantaneous
codes.

3. a. Derive the relation: = H(X) + H(Y)-HC,Y).(4)
0. Derive the chain rule of relative entropy for Markov source. (5)

PART B

4. a. Explain Noisy Type writer channel in detail. Find the capacity of the same with (6) noiseless
subset of inputs.

b. How the weakly symmetric channels are different from symmetric channels. (3)

5. a. Describe Data compression as a consequence of Asymptotic Equi-partition Property. (5)
b. Derive the capacity of a Binary channel, if a fraction 'p' is lost inthe channel. (4)

6. a. State and prove Joint Source-Channel coding theorem. (5)

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b. Mathematically state the properties of high probability set and typicalset. (4)