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 p n represent the probability that a binary symbol is in error after transmission through the complete system (a) Show that p n 1 (1 2p 1 ) n (b) If p i is very small and n is not too large, what is the corresponding value of p n

Question: Consider a chain of (n 1) regenerative repeaters, with a total of n sequential decisions made on a binary PCM wave, including the final

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 p₁ of being inverted by any repeater. Let p_n represent the probability that a binary symbol is in error after transmission through the complete system.

(a) Show that p_n = ½ [1 — (1 - 2p₁) ⁿ]

(b) If p_i is very small and n is not too large, what is the corresponding value of p_n?

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