Optical Bit Error Rate

Chapter 7 - Probability Theory of Bit Error Rate

7.1   INTRODUCTION

As data is transmitted over a medium, attenuation, combined noise, and jitter
sources all distort the shape of the transmitted bits, both in amplitude and time, to
such a degree that a receiver misinterprets some bit values and detects them wrongly;
that is, some logic “ones” are detected as logic “zeros” and some logic “zeros”
as logic “ones.” In communications, the number of error bits in the number of bits
transmitted provides a performance metric of the channel, from the transmitter to
(and including) the receiver. However, this metric needs clarification. For example,
if two data rates are 1 Mbit/s and 10 Gbit/s, 10 errors in a second mean
10/1,000,000 (or 10–5) and 10/10,000,000,000 (or 10–9) errors, respectively. Alter-
natively, 10 errors in 1,000,000 bits transmitted means 10 errors per second for the
1 Mbit/s rate and 100,000 errors per second for the 10 Gbit/s rate.

Thus, depending on performance limits set for a specific application, the channel
performance may or may not be acceptable. That is, the frequency (or rate) of erroneous
bits is very critical. Although it is impossible to predict if a particular bit will
be received correctly or not, it is possible to predict with good confidence the performance
of a channel if the parameters of the link are known, as well as the statistical
behavior (Gaussian, Poisson) of noise and jitter sources. Then, the frequency
of occurrence of erroneous bits and the signal-to-noise ratio can be reliably estimated.
What we have stated without having defined yet are the bit error ratio and the bit
error rate. What they are and what the difference between the two is is examined in
the next section. Thus, to model a transmission channel, a thorough knowledge is
required of the link from transmitter to receiver, including the transmission medium
and all components in between (Figure 7.1), as well as the sources of noise and jitter
(including linear and nonlinear multiwavelength interactions) and the laser and
photodetector characteristics.

In previous chapters, we discussed the light source and receiver, the medium,
loss and gain, and noise and jitter. In this chapter, our attention is focused on how
these degrading sources impact the value of a binary bit and change it from “one” to
“zero,” and “zero” to “one.” We estimate the probability of errors and we provide
an estimation methodology that can be implemented with an integrated solid-state
circuit, thus allowing for a continuous estimation at each port, and making cumbersome
measuring instruments necessary only for out-of-service precision testing.

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