SRM University 2007 B.Tech Electronics and Communications Engineering Bank of EC306-Information Theory - Question Paper

16. What is linear predictive coding and provide its use?





PART – B

1. A DMS “X” has six symbols x1, x 2, x3,x 4, x5, x6 with p(x1)=0.30,p( x 2)=0.25, p(x3)=0.20, p(x 4)=0.12,p(x5)=0.08,p(x6)=0.05.Construct a Huffman code for X and compute the code efficiency.


2. A DMS “X” has four symbols x1, x 2, x3,x four with p(x1)=1/2, p( x 2)=1/4, p(x3) =1/8, p(x 4) =1/8. Construct a Huffman code and compute the code efficiency.

3. A DMS “X” has five symbols x1, x 2, x3,x 4, x5, p(x1)=0.4,p( x 2)=0.19,p(x3)=0.16, p(x 4)=0.15,p(x5)=0.1.Construct a Huffman code for X and compute the code efficiency.

4. A DMS “X” has five symbols x1, x 2, x3,x 4, x5, p(x1)=0.2,p( x 2)=0.15,p(x3)=0.05, p(x 4)=0.1,p(x5)=0.5.Construct a Huffman code for X and compute the code efficiency.


5. A DMS has an alphabet of eight letters, x i,i=1,2,3,4,5,6,7,8,with probabilities 0.25,0.20,0.15,0.12,0.10,0.08,0.05 and 0.05.

a) Use the Huffman encoding procedure to determine a binary code for the source output.
b) Determine the avg. number R of binary digits per source letter.
c) Determine the entropy of the source and compare it with R.

6. The optimum 4 – level non uniform quantizer for a Gaussian – distributed signal amplitude outcomes in the 4 levels a1 ,a2 ,a3 ,and a4,with corresponding probabilities of occurrence p1 = p2 =0.3365 and p3 =p4 =0.1635.
a) Design a Huffman code that encodes a single level at a time and determine the avg. bit rate.
b) Design a Huffman code that encodes 2 output levels at a time and determine the avg. bit rate.
c) What is the minimum rate found by encoding J output levels at a time as J?8?


7. A DMS has an alphabet of eight letters, x i, i=1,2,3,4,5,6,7,8,with probabilities 0.25,0.20,0.15,0.12,0.10,0.08,0.05 and 0.05.
Use the Huffman encoding procedure to determine a ternary code (using symbols 0, one and 2) for encoding the source output.

8. obtain the Lempel – Ziv source code for the binary source sequence

10101101001001110101000011001110101100011011
Recover the original sequence back from the Lempel – Ziv source code.

9. It can be shown the rate – distortion function for a Laplacian source, px(x) = (2?)-1 e-¦x¦/? with an absolute value of fault - distortion measure

d(x,x)=¦x-x¦is provided by

Earning:   Approval pending.