Question: Show every step clearly with formula and explain all the logic.?Write clearly 6. Shannon code. Consider the following method for generating a code for a

Show every step clearly with formula and explain all the logic.?Write clearly

6. Shannon code. Consider the following method for generating a code for a random variable X which takes on m values {1, 2, ..., m} with probabilities P1, P2, ..., Pm. Assume that the probabilities are ordered so that P > P2 > ... > Pm. Define i-1 Fi = Pi = (1) k=1 the sum of probabilities of all symbols less than i. Then the codeword for i is the number F; [0, 1] rounded off to l; bits, where li = log 7. Pi (a) Construct the code for the probability distribution (0.5, 0.25, 0.125, 0.125). (b) Show that the code constructed by this process is prefix free and the average length satisfies H(X)

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