Information Theory and Coding 2018 Question Paper — Government Colleg…
The 2018 Information Theory and Coding previous year question paper (Government College of Engineering and Technology, Jammu), with every question and its marks.
- University: Government College of Engineering and Technology, Jammu
- Subject: Information Theory and Coding
- Course: Information Theory & Coding
- Branch: Electronics & Communication Engineering
- Year: 2018
- Paper: end-term
- Duration: 180 minutes
- Total marks: 100
Instructions
- Attempt five questions in all selecting at least two questions from each Section.
- Each question carries 20 marks.
- Use of calculator is allowed.
Questions
Section - A
- Q1. (a) Define source information rate. How it is related to information and entropy. (b) Consider a binary memoryless source X the two symbols $x_1$ & $x_2$. Prove that $H(x)$ is maximum when both $x_1$ and $x_2$ are equiprobable. [20 marks]
- Q2. (a) State and prove Shanon's Hartley theorem based on channel capacity. What is its significance? How does channel capacity change if bandwidth is increased to infinity? (b) Verify the following expression $I(x;y) = I(y;x)$. [20 marks]
- Q3. (a) Given a binary channel shown in Figure (i) Find the channel matrix of the channel (ii) Find $P(y_1)$ and $P(Y_2)$ when $P(x_1) = P(x_2) = 0.5$ (iii) Find joint probability $P(x_1, y_2)$ and $P(x_2, y_1)$ when $P(x_1) = P(x_2) = 0.5$ (b) Find the channel capacity of the binary erasure channel. [20 marks]
- Q4. (a) A DMS X has five symbols $x_1, x_2, x_3, x_4, \& x_5$ with probabilities $P(x_1) = 0.4, P(x_2) = 0.19, P(x_3) = 0.16, P(x_4) = 0.15$ and $P(x_5) = 0.1$. Construct Huffman code and calculate the efficiency of the code. (b) A channel has a Bandwidth of 8kHz, what is channel capacity if signal to noise ratio being 31 for same channel capacity, if signal to noise ratio is increased to 61, then what will be the new channel bandwidth? [20 marks]
Section - B
- Q5. (a) Define the following terms: (i) Code word (ii) Block Length (iii) Code rate (iv) Channel data rate (v) Code vectors (b) Design a linear block code with a minimum distance 3 and a message block size of 8 bits. [20 marks]
- Q6. (a) Give the performance comparison of convolution codes and block codes. (b) Determine the encoded message for the following 8 bit data code using the CRC generating polynomial: $P(x) = x^4 + x^3 + x^0$, Data code - $11\ 00\ 11\ 00$ [20 marks]
- Q7. (a) Explain soft decision decoding with suitable example. (b) Use viterbi algorithm to decode the sequence $1\ 00\ 110\ 111\ 101\ 001\ 101\ 001\ 010$. Compare the convenience of code tree, trellis diagram and state diagram from encoding and decoding of convolutional codes point of view. [20 marks]
- Q8. Write short notes on: (a) Non binary block codes (b) Cyclic codes [20 marks]