Important Questions in Information Theory and Coding IT2302 IT 2302 - subject for NOV/DEC 2011 ANNA UNIVERSITY EXAMINATIONS FOR III YEAR IT Students

IT2302 - Information Theory and Coding

UNIT I

- Encode the following messages with their respective probability using basic Huffman algorithm:

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 |

1/2 | 1/8 | 1/8 | 1/16 | 1/16 | 1/16 | 1/32 | 1/32 |

Also calculate the efficiency of coding and comment on the result

2. State and prove the source coding theorem

3. State and prove the properties of mutual information.

4. Two BSCs are connected in cascade as shown in Fig.

Find the channel matrix of the resultant channel. Find P(z1) if P(x1)= 0.6 and P(x2)= 0.4

UNIT II

**1. **With the following symbols and their probability of occurrence encode the message “rose#” using arithmetic coding algorithm.

Symbols | r | o
| s | e | # |

Probability | .1 | .3 | .2 | .3 | .1 |

2. Explain Linear Predictive Coding

3. With the block diagram explain DPCM system. Compare DPCM & ADPCM systems.

4. With a block diagram explain psychoacoustic model

UNIT III

1. Explain the JPEG encoder in detail.

2. Explain the compression principles of P and B frames

3. Explain the principles of perceptual coding.

4. Explain the concept of LPC and MPEG layers

UNIT IV

1. For a systematic linear block code, the three parity-check bits *c4, c4, c6* are formed from the following equations:

*c*_{4} = d_{1} *Å** d*_{3} ; c_{5}=d_{1}*Å** d*_{2} *Å** d*_{3}; c_{6} = d_{1}*Å** d*_{2}

(i)Write down the generator matrix (5)

(ii)Construct all possible code words. (5)

(iii)Suppose that the received word is **01011**. Decode this received word by finding the location of the error and the transmitted data bits

2. Determine the encoded message for the following 8- bit data codes using the CRC generating polynomial p(n)= *x*^{4}+x^{3}+x^{0}.

(i)11001100 (ii)01011111

3. Consider the (7, 4) Hamming code defined by the generator polynomial *g(x) = 1+x+x*^{3}. The code word 1000101 is sent over a noisy channel, producing the received word 0000101 that has a single error. Determine the syndrome polynomial *s(x)* for this received word. Find its corresponding message vector *m *and express *m *in polynomial *m(x*).

4. Consider a (7,4) cyclic code with generator polynomial *g(x)= 1+x+x*^{3}. Let data* d= (1010). *Find the corresponding systematic code word.

UNIT V

1. Construct a convolutional encoder for the following specifications: rate efficiency ½, constraint length 3, the connections from the shift register to modulo – 2 adder are described by the following equations,

*g*_{1}(x) =1+x+x^{2}, g_{2}(x)=1+x^{2}.Determine the output codeword for the message [10011]

2. A rate 1/3 convolution encoder has generating vectors as g_{1}= (100), g_{2}= (111), g3= (101)

(i)Sketch the encoder configuration.

(ii)Draw the code tree, state diagram and trellis diagram.

(iii)If the message sequence is 10110, determine the output sequence of the encoder

3. A convolution encoder has a single shift register with 2 stages, 3 mod-2 adders and an output Mux. The generator sequence of the encoder as follows: g^{(1)}=(1,0,1), g^{(2)}=(1,1,0) g^{(3)}=(1,1,1). Draw the block diagram and encode the message sequence (1110) and also draw the state diagram.

4. Explain the Turbo Decoding in detail.

Thank you sir.......

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