Important RGPV Question
EC-702 (B) Information Theory and Coding
VII Sem, EC
Unit I Information Theory
Q.1 Define uncertainty, information and entropy. Show that the entropy is maximum when all the message are equi-probable. Assume M = 3. (RGPV Nov 2023)
Q.2 The international Morse code uses a sequence of dots and dashes to transmit letters of the English alphabet. The dash is represented by a current puise that has a duration of 3 units and the dot has a duration of 1 unit. The probability of occurrence of a dash is 1 of the probability of occurrence of a dot.
i) Calculate the information content of a dot and a dash.
ii) Calculate the average information in the dot-dash code.
iii) Assume that the dot lasts I m sec, which is the same time interval as the pause between symbols.
Find the average rate of information transmission. (RGPV Nov 2023)
Q.3 Discuss uncertainty, entropy with its properties as per theory of information. (RGPV Dec 2020)
Unit II Coding theorem
Q.1 Show that I (X; Y) = H (X) + H (Y)-Η (Χ, Υ). 1 (RGPV Nov 2023)
Q.2 Explain general form of a decoder for cyclic codes with error correction procedure. (RGPV Nov 2023)
Q.3 Construct the I luffman code with minimum code variance for the following probabilities and also determine the code variance and code efficiency: (0.25, 0.25. 0.125, 0.125, 0.125, 0.0625, 0.0625). (RGPV Nov 2023)
Q.4 Discuss about arithmetic coding with suitable example. (RGPV Nov 2023)
UNIT III Information Channels
Q.1 ABSC has the error probability p = 0.21 and the input to the channel consists of 4 equiprobable messages x_{1} = 0 x_{2} = 0l x_{3} = 11 x_{4} = 111
Calculate:
i) p(0) and p(1) at the input
ii) Efficiency of the code
iii) Channel capacity
(RGPV Nov 2023)
Q.2 From channel capacity theorem, find the capacity of a channel with infinite bandwidth and explain. (RGPV Nov 2023)
Q.3 Discuss the Binary Erasure Channel (BEC) and also derive channel capacity equation for BEC. (RGPV Nov 2023)
Q.4 Derive the Channel Capacity of Binary Erasure Channel. (RGPV Dec 2020)
Q.5 A very noisy symmetric binary channel is able to transmit 1000 bits per second, but has a 25% probability of introducing error into each bit transmitted. What is the channel capacity in bits per second? (RGPV Dec 2020)
Q.6 Show that mutual information is symmetric. (RGPV Dec 2020)
Q.7 Prove that the average code-word length E(w) of a binary instantaneous code for discrete memory less source with entropy H(X) satisfies the inequality H(X) ≤ E(W ) < H(X) + 1. (RGPV Dec 2020)
Q.8 Derive the channel capacity of band limited Gaussian channels. (RGPV Dec 2020)
UNIT IV Error Control Coding
Q.1 The generator matrix for a (6, 3) block code is given below. Find all code vectors of this code. (RGPV Nov 2023)
Q.2 Design (n, k) hamming code with a minimum distance of d tmin =3 and message length of 4 bits. (RGPV Nov 2023)
Q.3 A (7, 4) cyclic code has a generator polynomial: g(X)=X+X+1. (RGPV Nov 2023)
i) Draw the block diagram of encoder and syndrome calculator.
ii) Find generator and parity check matrices in systematic form.
Q.4 State and prove Kraft inequality. (RGPV Dec 2020)
Q.5 Give example for a Hamming code. Write down generator matrix and parity check matrix of that code. Comment on the error correction capability of the Hamming Code. (RGPV Dec 2020)
Q.6 Explain generation of systematic cyclic code. (RGPV Dec 2020)
Q.7 Obtain the standard array of the linear block code with code words C = {0000, 1001, 0110, 1111}. (RGPV Dec 2020)
Q.8 What are different types of errors? Explain them with suitable examples. (RGPV Dec 2020)
UNIT V Introduction to BCH codes
Q.1 Explain the working of (2,1,3) Convolutional encoder using transform domain approach. (RGPV Nov 2023)
Q.2 Explain BCH codes in details with taking a suitable example. (RGPV Nov 2023)
Q.3 The Viterbi algorithm used for decoding of convolution codes is an example of Maximum likelihood decoding. Explain. (RGPV Dec 2020)
Extra Questions
Q.1 Write a short notes on any two: (RGPV Nov 2023)
i) Lempel-Ziv Coding
ii) Code Tree
iii) Viterbi Algorithm
iv) Extended Huffman Coding
Q.2 Show that the mutual information I(X; Y) ≤ 0. Under what condition does the equality hold? (RGPV Dec 2020)
Q.3 Write brief notes on (RGPV Dec 2020)
i) Trellis and state diagrams
ii) Channel Models and its Matrix
Q.4 Comment on the following: Lempel-Ziv Coding , Error correction capabilities of linear block codes.(RGPV Dec 2020)
— Best of Luck for Exam —
