1. A source emits seven symbols x1, x2, ... x7 with probabilities 0.35, 0.3, 0.2, 0.1, 0.04, 0.005, 0·005 respectively. Give Huffman coding for these symbols and calculate average bits of information and average binary digits of information per symbol.

2.(a) Prove the code-word lengths of any uniquely decodable code must satisfy the Kraft; inequality Let have the following joint distribution <img src='./qimages/10970-2b.jpg'>

Find
3.(a) Derive the relationship between entropy and mutual information. Draw a Venn diagram for that relation.

(b) Prove for non-negative numbers a1, a2 ... an and b1, b2, ... bn <img src='./qimages/10970-3b.jpg'>

with equality if and only if ai/bi constant.

4.(a) Prove, if V1, V2,... Vn is a finite alphabet stochastic process that satisfies the AEP, then there exists a source channel code with if C.
Show that any sequence of codes with 0 must have R C.

5. Consider a code whose generator matrix is
<img src='./qimages/10970-5.jpg'> Find all the code-words of the code. Find the parity-check matrix of the code. Compute the syndrome for the received vector 1101101.

6. What is the symbol-error correcting capability of a R-S code How many bits are there per symbol Compute the number of rows and columns in the standard array required to represent the R-S code. How much residual symbol-error correcting capability does it have?

7. For MPSK modulation, bandwidth efficiency increases with higher-dimensional signalling but for MFSK, it decreases. Explain the reason thereof.

8. Explain Hamming code. How many Hamming bits are required for a block length of 20 message bits to correct a 1-bit error Demonstrate it with the help of an example.

9. Calculate the rate of joint information transmission for the channel below:

<br><br> <img src='./qimages/10970-9.jpg'>

Assume where x2} is the set of input symbols.

Assume q Probability of correct reception,
p Probability of incorrect reception, be the set of received symbols.

10. Write short notes on any two of the following:

(a) Reed Solomon Codes
Shannon's Channel Coding Theorem
Characteristics of Finite Fields