Information Theory Coding And Cryptography

a) What is Entropy? Show that the entropy is maximum when the entire message is equi-probable. Assume M = 3.

b) Explain redundancy and uncertainty.

a) Write a short note on Random variable and their properties.

b) Write short note on:

1. Discrete-Time Birth-Death Processes
2. Statistical independence

a) Explain Cyclic Redundancy Check with suitable example.

b) Explain decoding of BCH codes with suitable example.

a) Describe RSA algorithm. What attacks are possible in the RSA algorithm?

b) Consider a (7, 4) block code generated by:

$$ G=\begin{bmatrix} 1 & 0 & 0 & 0 & : & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & : & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 & : & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & : & 1 & 1 & 1 \end{bmatrix} $$

Explain how the error syndrome S helps in correcting a single error.

a) The generator matrix for a (6, 3) block code is given below. Find all code vectors of this code

$$ G=\begin{bmatrix} 1 & 0 & 0 & : & 1 & 1 & 0 \\ 0 & 1 & 0 & : & 0 & 1 & 1 \\ 0 & 0 & 1 & : & 1 & 1 & 1 \end{bmatrix} $$

b) The generator polynomial of a (7, 4) cyclic code is g(x) = 1 + x + x³. Find the 16 code words of this code.

a) Find all the cyclic binary codes of block length 5. Find the minimum distance of each code.

b) What do you mean by soft and hard decoding and viterbi algorithm?

a) What do you understand by turbo coding?

b) Differentiate between the following terms:

1. Confusion and Diffusion
2. Substitution cipher and transposition cipher

Write short notes on any two of the following:

1. Division algorithm
2. Encryption techniques and algorithms
3. Cryptography
4. Diffusion and confusion