The capacity of digital links in tandem

Suppose we haveLdigital links in tandem. Between successive links we have a repeater. The links are each white Gaussian channels with no bandwidth constraint. The repeater may either be a {em binary repeater}, which sends on each bit separately having made a binary decision on each, or a {em Shannon repeater}, which perfectly reproduces at one end the bits that were transmitted at the other end of the link. What is the loss in capacity if we use only binary repeaters and code for the entire L links at the transmit end? For largeL, the capacity drops by a factor asymptotic to InL, and the normalized optimum timeTper symbolT_{opt}^{L}is also asymptotic toln L. Arbitrarily shortLgives0capacity forL > 1. More precise asymptotic results are obtained and compared with computed numerical values. These results show when it pays to code each link separately in digital data transmission.