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Consider a chain of (n - 1) regenerative repeaters, with a total of n sequential decisions made on a binary PCM wave, including the final decision made at the receiver.
Assume that any binary symbol transmitted through the system has an independent probability p_{1} of being inverted by any repeater. Let pn represent the probability that a binary symbol is in error after transmission through the complete system.
a. Show that
b. If p_{1} is very small and n is not too large, what is the corresponding value of p_{n}?