# Consider a chain of (n — 1) regenerative repeaters, with

# Consider a chain of (n — 1) regenerative repeaters, with

Consider a chain of (n â 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 pn represent the probability that a binary symbol is in error after transmission through the complete system.

(a) Show that pn = ?1 [1 â (1 – 2p1) n]

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