SPPU Electronics and Telecom Engineering (Semester 6)
Information Theory and Coding Techniques
May 2017
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

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.
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.
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 tc1, 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
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
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.
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.
i) Drawtrellis diagram.
ii) Find dfree 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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