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A source transmitted a message through a noisy channel

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A source transmitted a message through a noisy channel. Each symbol is 0 or 1 with probability p and 1 - p, respectively and is received incorrectly with probability eo and E1. Errors in different symbol transmission are independent

(a) What is the probability that the kth symbol is received correctly?

(b) What is the probability that the string of symbols 0111 is received correctly?

(c) To improve reliability, each symbol is transmitted three times and the received string is decoded by majority rule. For example, a 0 is transmitted as 000 and is decoded at the receiver as a 0 if and only if the received three symbol string contains at least two Os. Similar rule applies to 1. What is the probability that a 0 is corrected decoded?

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