Question: A discrete, memoryless source emits a sequence of statistically independent binary digits with probabilities p1 = 0.005 and p0 = 0.995. The digits are taken

A discrete, memoryless source emits a sequence of statistically independent binary digits with probabilities p1 = 0.005 and p0 = 0.995. The digits are taken 100 at a time, and a binary codeword is provided for every sequence of 100 digits containing three or fewer ones.

(a) Assuming that all codewords are the same length, find the minimum length required to provide codewords for all sequences with three or fewer ones.

(b) Calculate the probability of observing a source sequence for which no codeword has been assigned.

(c) Use Chebyshev's inequality to bound the probability of observing a source sequence for which no codeword has been assigned.

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