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Pages: 2

Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Seventh Semester B.Tech Degree Examination (Regular and Supplementary), December 2020

Max. Marks: 100

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Course Code: EC401
Course Name: INFORMATION THEORY & CODING

PARTA
Answer any two full questions, each carries 15 marks.
Find the self information of two messages with respective probabilities 0.1 and
0.9. Comment on the results.
Prove that mutual information of a channel is symmetric and always non-

negative.

Joint probability matrix of a discrete channel is given below:
0.3 0.2 0.1

P(X,Y)=
0.1 0.1 0.2

Determine the different entropies and verify their relationships.
State and prove noiseless coding theorem.

An analog signal is band limited to 3.4 kHz and is sampled at Nyquist rate. The
samples are quantized into 4 levels. The quantization levels are assumed to be

independent and occur with probabilities ற, = 4; ‏وم‎ =; p; = py %. Find the
information rate of the source.
Find binary Huffman code for random variable S = (51, 52, 53, 54, 55, 56, 57. Ss}
with probabilities (0.4, 0.25, 0.15, 0.06, 0.05, 0.04, 0.03, 0.02}. Move the
combined symbol as high as possible. Find average code word length and
efficiency.
Consider a message ensemble 5 = (91, 52, 53, 54, 55, 56) with probabilities P =
{1/3, 1/4, 1/8, 1/8, 1/12, 1/12}. Construct a binary code and determine its
efficiency using Shannon — Fano coding procedure.
Explain binary symmetric and binary erasure channels. Derive the expression for
their channel capacities.
PART ந

Answer any two full questions, each carries 15 marks.
What are the properties to be satisfied by a linear block code? Illustrate with an
example.
What is the capacity of a channel of infinite bandwidth?

Define the terms Hamming weight, Hamming distance and minimum Hamming
distance with suitable example.
Explain band width — SNR trade off in a Gaussian channel.

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Duration: 3 Hours

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