In order to increase the probability of correct transmission of a message overa noisy

Chapter 1, Problem 3

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In order to increase the probability of correct transmission of a message overa noisy channel, a repetition code is often used. Assume that the messageconsists of a single bit, and that the probability of a correct transmission on asingle trial is p. With a repetition code of rate 1/n, the message is transmitted afixed number (n) of times and a majority voter at the receiving end is used fordecoding. Assuming n = 2k + 1, k = 0, 1, 2 ..., determine the error probabilityPe of a repetition code as a function of k.

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