Appendix D
Ultimate System Capacity
With the advent of wavelength-division multiplexing (WDM) technology, lightwave
systems with a capacity of more than 1 Tb/s have become available commercially.
Moreover, system capacities in excess of 10 Tb/s have been demonstrated in several
laboratory experiments. Every communication channel has a finite bandwidth, and
optical fibers are no exception to this general rule. One may thus ask: What is the
ultimate capacity of a fiber-optic communication system? This appendix focuses on
this question.
The performance of any communication system is ultimately limited by the noise
of the received signal. This limitation can be stated more formally by using the concept
ofchannel capacityintroduced within the framework of information theory [1]. It turns
out that a maximum possible bit rate exists for error-free transmission of a binary digital
signal in the presence of Gaussian noise. This rate is called the channel capacity. More
specifically, the maximum capacity of a noisy communication channel is given by
Cs=∆fchlog 2 ( 1 +S/N), (D.1)where∆fchis the channel bandwidth,Sis the average signal power, andNis the average
noise power. Equation (D.1) is valid for a linear channel with additive noise. It shows
that the system capacity (i.e., the bit rate) can exceed the bandwidth of the transmission
channel if the noise level is low enough to maintain a high signal-to-noise ratio (SNR).
In fact, it is common to define the spectral efficiency of a communication channel as
ηs=Cs/(∆fch)that is a measure of bits transmitted per second per unit bandwidth and
is measured in units of (b/s)/Hz. For a SNR of>30 dB,ηsexceeds 10 (b/s)/Hz.
Equation (D.1) does not always apply to fiber-optic communication systems be-
cause of the nonlinear effects occurring inside optical fibers. It can nonetheless be
used to provide an upper limit on the system capacity. The bandwidth∆fchof mod-
ern lightwave systems is limited by the bandwidth of optical amplifiers and is below
10 Tb/s (80 nm) even when both the C and L bands are used simultaneously. With
the advent of new kinds of fibers and amplification techniques, one may expect that
eventually∆fchwill approach 50 THz by using the entire low-loss region extending
from 1.25 to1.65μm. The SNR should exceed 100 in practice to realize a bit-error rate
below 10−^9. Using these values in Eq. (D.1), the maximum system capacity is close to