SPPU Electronics and Telecom Engineering (Semester 6)

Information Theory and Coding Techniques

May 2017

Information Theory and Coding Techniques

May 2017

Solve any one question from Q.1(a,b,c) &Q.2(a,b,c)

1(a)
The joint probability marix representing transmitter and receiver is given below. Find all entropies and mutual information of the communication system \[P(X, Y)=\begin{bmatrix}
0.3& 0.05&0 \\
0 & 0.25&0 \\
0 & 0.15 &0.05 \\
0& 0.05 &0.15
\end{bmatrix}\]

6 M

1(b)
Obtain the coding efficiency of a Shannon Fano for a zero memory sources that emits eight messages with respective probabilities as given below. Use 3 letters for encoding such as -1, 0, 1. \[P = \left [ 0.3\ \ 0.12 \ \0.12\ \ 0.12\ \ 0.12\ \ 0.08\ \ 0.07\ \ 0.07 \right ]\\
X=\left [ X_{1}\ \ X_{2}\ \ X_{3}\ \ X_{4}\ \ X_{5}\ \ X_{6}\ \ X_{7}\ \ X_{8} \right ] \]

6 M

1(c)
Explain the case study related to application of Huffman's coding and JPEG in image compression.

8 M

2(a)
The Party check matrix of a (7, 4) Hamming Code is given below: \[\begin{bmatrix}
1 & 1 & 1&0 & 1 & 0 &0 \\
0 &1 &1 & 1 &0 & 1 &0 \\
1 &1 & 0 & 1 & 0& 0 & 1
\end{bmatrix}\]

i) Find Generator Matrix.

ii) Find out all possible codewords.

iii) Determine error correcting capability of the code.

i) Find Generator Matrix.

ii) Find out all possible codewords.

iii) Determine error correcting capability of the code.

7 M

2(b)
Consider (7,4) cyclic code: with \( g(x)=x^{3}+x+1. \)/

i) Draw the hardware arrangement of cyclic encoder and verify the encoder by considering one message

ii) If received code vector is 1001101, findout transmitted or corrected codeword.

i) Draw the hardware arrangement of cyclic encoder and verify the encoder by considering one message

ii) If received code vector is 1001101, findout transmitted or corrected codeword.

7 M

2(c)
Explain any two properties of mutual information and show that Shannon's limit for AWGN Channel is -1.6dB.

6 M

Solve any one question from Q.3(a,b,c) &Q.4(a,b,c)

3(a)
Find generator polynomial for BCH code over GF (16) using primitive polynomial \(P(x)=x^{2}+x+2 \)/ over GF(4) codeword. The code should correct t

_{c}1, 2 errors. The addition and multiplication tables are as given below: !mage
8 M

3(b)
Write short notes on

i) CRC codes

ii) Golay Codes

i) CRC codes

ii) Golay Codes

6 M

3(c)
Explain FEC technique for Erro Control.

4 M

4(a)
Explain the steps of BCH decoding with Georenisein Zierler Algorithm.

6 M

4(b)
Explain the application of RS codes and CRC code.

6 M

4(c)
Distinguish between BCH and RS codes.

6 M

Solve any one question from Q.5(a,b) &Q.6(a,b)

5(a)
Explain the following:

i) Code Rate

ii) Constraint Length

iii) Word Length

iv) Block Length

v) Free Distance

vi) Hamming Distance

i) Code Rate

ii) Constraint Length

iii) Word Length

iv) Block Length

v) Free Distance

vi) Hamming Distance

12 M

5(b)
What are Turbo Codes? Explain the coding and decoding of Turbo codes.

4 M

6(a)
For the convolution encoder shown in fig below, construct the Code tree and trellis digram, find out the out of the encoder corresponding to message sequence 10110 using trellis.

!mage

!mage

10 M

6(b)
Explain Sequential decoding and Viterbi decoding.

6 M

Solve any one question from Q.7(a,b) & Q.8(a,b,c)

7(a)
What are the Ungerboek's TCM design rules. Explain asymptotic coding gain.

6 M

7(b)
Coonsider the 8 state, 8PSK TCM scheme as shown below.

!mage

i) Drawtrellis diagram.

ii) Find d

!mage

i) Drawtrellis diagram.

ii) Find d

_{free}and Asymptotic coding gain and comment on it.
10 M

8(a)
Discuss Mapping by Set partitioning.

6 M

8(b)
Explain Euclidean distance, Asymptotic coding gain of trellis coded Modulation.

4 M

8(c)
Draw and explain the band limited and power limited coding system.

6 M

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