A 10000EC401122101 Pages: 2

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Seventh Semester B.Tech Degree Regular and Supplementary Examination December 2021 (2015 Scheme)

Course Code: EC401
Course Name: INFORMATION THEORY & CODING
Max. Marks: 100 Duration: 3 Hours
PARTA
Answer any two full questions, each carries 15 marks. Marks

1 a) Define the term marginal entropy and give its units? What will be the marginal (5)
entropy if a source emits all the M messages with equal probability?

b) Let X and Y be two discrete random variables and their joint probability is given (10)

by
.08 .15 .11
_ |.06 .09 .14
2൦502 03 06
.13 .09 .04

Find marginal, conditional and joint entropies and verify the relation.
2 a) State and prove Kraft’s inequality (7)
b) Two symbols 51, x2 with probabilities P(x;) = 0.4 and P(x2) = 0.6 are transmitted (8)
through a discrete channel given below.

P(Y/X)= 0.8 |.

0.2 0.8
Identify the channel and calculate the capacity and the efficiency of the channel.

3 ஐ Define mutual information I(X; ४). Find the mutual information if X and Y are (5)
independent.

b) A discrete source emits 7 symbols with probabilities, 0.15, 0.24, 0.13, 0.26, 0.12, (19)
0.02, 0.08. Construct binary codes using Huffman algorithm and Shannon Fano
algorithm. Compare the efficiencies of these two codes.

PART ‏تا‎
‎Answer any two full questions, each carries 15 marks.
4 a) Find the differential entropy of a Gaussian distributed random variable. (7)

b) Derive the capacity of a Gaussian channel with bandwidth B and noise power (8)
spectral density N/2. Also, find the capacity when the bandwidth of the channel

tends to infinity.

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