B.TECH - Semester 7 information theory and coding Question Paper 2013 (dec)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Define mutual information $X(X ; Y)$ between two random variable X and Y .
- Define efficiency and redundancy of a source code.
- In a binary Huffman code, there will always be two codewords of maximum length. Why?
- Write down channel transition matrix of a binary erasure channel.
- Define rate distortion function.
- Determine the channel capacity of a channel whose probability transition matrix is given by $P(Y / X)=\left[\begin{array}{ll}4 / 5 & 1 / 5 \\ 1 / 5 & 4 / 5\end{array}\right]$.
- Give an example of a Galois field. What are its properties?
- Define perfect codes. Give an example.
- What is secret key cryptography?
- What is constraint length of a convolutional code? $$ \text { ( } 10 \times 2=20 \text { Marks) } $$ P.T.O. Answer one question from each module. Each question carries 20 marks.
- The joint probability mass function of two random variables $X$ and $Y$ is given by | | $y_{1}$ | $y_{2}$ | $y_{3}$ | | :---: | :---: | :---: | :---: | | | | | | | $\mathrm{x}_{1}$ | $3 / 40$ | $1 / 40$ | $1 / 40$ | | $\mathrm{x}_{2}$ | $1 / 20...
- The joint probability mass function of two random variables $X$ and $Y$ is given by | | $y_{1}$ | $y_{2}$ | $y_{3}$ | | :---: | :---: | :---: | :---: | | | | | | | $\mathrm{x}_{1}$ | $3 / 40$ | $1 / 40$ | $1 / 40$ | | $\mathrm{x}_{2}$ | $1 / 20...
- The joint probability mass function of two random variables $X$ and $Y$ is given by | | $y_{1}$ | $y_{2}$ | $y_{3}$ | | :---: | :---: | :---: | :---: | | | | | | | $\mathrm{x}_{1}$ | $3 / 40$ | $1 / 40$ | $1 / 40$ | | $\mathrm{x}_{2}$ | $1 / 20...
- A discrete memory less source emits symbols from an alphabet containing $A, B$, $C, D, E, F$ and $G$ with probabilities $1 / 3,1 / 27,1 / 3,1 / 9,1 / 9,1 / 27,1 / 27$ respectively. Construct a source code using (a) Shannon-Fano procedure and
- A discrete memory less source emits symbols from an alphabet containing $A, B$, $C, D, E, F$ and $G$ with probabilities $1 / 3,1 / 27,1 / 3,1 / 9,1 / 9,1 / 27,1 / 27$ respectively. Construct a source code using (b) Huffman procedure. Determine the ef...
- (a) State Shannon-Hartley theorem.
- (b) Derive the Shannon limit -1.6 dB for a band-limited AWGN channel.
- (c) Explain significance of Shannon limit using a plot between SNR per bit and bandwidth efficiency.
- (a) Define (i) a discrete memoryless channel (ii) a channel code for a discrete memoryless channel and (iii) rate of a channel code.
- (b) State Shannon's noisy coding theorem.
- (c) Derive the formula for the channel capacity of a binary symmetric channel. 20
- (a) Explain the procedure for constructing standard array of a linear block code.
- (b) Show that no vector will appear twice in a standard array.
- (c) Describe how decoding is done using standard array.
- (a) Parity check matrix of a linear block code is given by $$ H=\left[\begin{array}{lllllll} 0 & 0 & 1 & 1 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 & 1 \\ 1 & 0 & 0 & 1 & 1 & 1 & 0 \end{array}\right] $$
- (i) Determine generator matrix G . (ii) Use the generator matrix to encode the message ( 0100 ). (iii) Determine the minimum distance of the code (iv) Construct the table of syndromes for the code.
- (b) $A(7,4)$ cyclic code has generator polynomial $g(X)=1+X+X^{3}$. Find the code polynomial and codeword in systematic form for the message (1010).
- (a) $A(2,1,3)$ convolutional code has generator matrix defined by $g^{(1)}=\left(\begin{array}{lll}1 & 1 & 1\end{array}\right)$ and $g^{(2)}=(101)$. Write down its generator matrix. Find the output using both time-domain approach and polynomial-domai...
- (b) Describe the DES algorithm. OR
- (a) Sketch the diagram of a $(2,1,4)$ convolutional encoder with rate half and constraint length 4 , given that $g^{(1)}=(1101)$ and $g^{(2)}=(1111)$.
- (b) Explain maximum-likelihood decoding of convolutional codes.
- (c) Describe Viterbi decoding for the above code using trellis diagram. $$ (4 \times 20=80 \text { Marks }) $$