# RTU Previous Question Papers BE 4th Semester

# Information Theory and Coding July 2011

**UNIT-I**

1.(a) Define Entropy. Show that the entropy is maximum when all the messages are equiprobable. Assume M = 3.

(b) A Random Variable has a density function as shown below. Find the corresponding entropy.

**OR**

2. (a) In a message conveyed through a long sequence of dots and dashes, the probability of occurrence of a dash is one third of that of a dot. the duration of a dash is three times that of a dot. If the dot lasts for 10 m sec. and the same time is allowed between symbols, determine the following :

(i) The information in dot and dash

(ii) Average information in the dot-dash code

(iii) Average information rate.

(b) Give differences between Discrete and Continuous communication channel.

**UNIT II**

3. (a) State Shannon Hartley Theorem. Give its implications.

(b) Define Transformation. Prove that the transinformation of a continuous system is non-negative.

**OR**

4. (a) Prove that the channel capacity of a white-bandlimited Gaussian channel is C = w log f 1 it i s,

N. where w = Channel Bandwidth S/N = Signal to Noise Ratio.

(b) A Gaussian channel has 1 MHz bandwidth. Calculate the channel capacity if its signal power to (two sided) noise spectral density ratio is 5 x 10^{4} Hz. Also find the maximum information rate.

**UNIT III**

5 (a) State Kraft’s inequality.

(b) Define the following terms :

(i) Source coding

(ii) Channel coding

(iv) Entropy coding.

(c) Explain Error Control coding with the help of a suitable diagram.

6 (a) Explain the following with suitable example :

(1) Variable Length Code

(ii) Prefix Free Code

(iii) Uniquely Decodable Code

(v) Instantaneous Code.

(b) Explain ARQ and FEC methods of Error Control Coding. List their advantages and disadvantages.

**UNIT IV**

7 (a) Given a (7,4) code with g(x) = x^{3} + x^{2} + l, construct the decoding table for this single error correcting code.

(b) Determine the data vector transmitted for the received vector, r = 1101101

**OR**

8. Consider the following (k+1, k) systematic LBC, with the parity check digit, C^_{+}^ given by C, = d. © d~ ©© d,. A’+l I 2 k

(a) Construct appropriate generator matrix for this code.

(b) Construct the code generated by this matrix for k = 3.

(c) Determine the error correcting and error detecting capability of this code.

(d) Show that CH^{t} = 0 and rH = 0 if no error occurs 1 if error occurs

**UNIT – V**

9 (a) Compare coded and uncoded systems in terms of Probability of Error

(b) Write short note on :

(i) Interlaced Code

(ii) Sequential Coding.

**OR**

10 (a) For the convolutional Encoder shown below

(i) Draw the state diagram

(ii) Draw the trellis diagram

(iii) Determine the o/p sequence for the input data, d = 11010100.