Run-length coding. Let X1, X2, …, Xn be (possibly dependent) binary random variables. Suppose that one calculates the run lengths 𝐑=(R1, R2, …) of this sequence (in order as they occur). For example, the sequence 𝐗=0001100100 yields run lengths 𝐑=(3,2,2,1,2) . Compare H(X1, X2, …, Xn), H(𝐑), and H(Xn, 𝐑) . Show all equalities and inequalities, and bound all the differences. | Numerade
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SOLVED: A run-length coder segments a binary information sequence into strings that consist of either a run of k zeros punctuated by a one for k > 0, m > 1, or a string of m zeros. For example, for the m = 3 case, possible strings and their corresponding run-lengths are given in the following table:String Run-length k01 001 000Suppose that the information sequence is produced by a sequence of Bernoulli trials with P(one) = P(success) = p. Let X be the run-length for a given string
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