What is meant by uniquely decidable code?

Write a comparative note on Huffman code and Shannon's codes.

2. Prove that for any instantaneous code (prefix code) over an alphabet size the codeword length I1,I2, ....., Im must satisfy the inequality Ei 1. Also prove that for a given set of codeword lengths that satisfy this inequality, there exists an instantaneous code with these word lengths.

Discuss the various properties of differential entropy and mutual information.

Let U be a memoryless source taking values in with the probabilities .

{0·4, 0·2, 0·15, 0·1, 0·05, 0·05, 0·05}
respectively. Find the entropy of U.

Discuss briefly about the importance of Reed-Solomon codes.

Prove that a cyclic code has a unique complement that is also cyclic.

Explain, why BCH codes are not suitable in cases of compact discs, digital audio tapes and other data storage systems.

Prove that a BCH code of designed distance B has minimum weight at least B.

6. What do you mean by band limited channel? Discuss its utility in communication over a radio network.

7. Derive an expression to prove the fact that the entropy of a pair of random variables is the entropy of one plus the conditional entropy of the other.

Discuss the basic properties of finite fields and the prerequisite conditions for its construction.

Describe briefly about the error detection and correction codes.

9. Write short notes on any two of the following

Error Probability Plane

M-ary Signalling

Bandwidth Efficient Modulation

10. The input source to a noisy communication channel is a random variable X over the four symbols c and d. The output from this channel is a random variable Y over these same four symbols. The joint distribution of these two random variables is given in the following table
x=a x=b x=c x=d

y=a 1/8 1/16 1/16 1/4
y=b 1/16 1/8 1/16 0
y=c 1/32 1/32 1/16 0
y=d 1/32 1/32 1/16 0

Find the mutual information I between the two random variables in bits.