Course Solutions Uncategorized (Solved) : C Entropy H Bits Following Source Alphabet Whose Letters Probabilities Shown 1 4 1 8 1 2 1 Q33095103 . . . .

(Solved) : C Entropy H Bits Following Source Alphabet Whose Letters Probabilities Shown 1 4 1 8 1 2 1 Q33095103 . . . .

 

C(a) What is the entropy H. in bits, of the following source alphabet whose letters have the probabilities shown? ВС 1/4 1/8 1/2 1/8 (b) Why are fixed length codes inefficient for alphabets whose letters are not equiprob- able? (c) Offer an example of a uniquely decodable prefix code for the above alphabet which is optimally efficient. What features make it a uniquely decodable prefix code? (d) What is the coding rate R of your code? How do you know whether it is optimally etticient? (e) What is the maximum possible entropy H of an alphabet consisting of N different letters? In such a maximum entropy alphabet, what is the probability of its most likely letter? What is the probability of its least likely letter?C(a)

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