# Appendix B. Calculation of Quality Factor Q

```Appendix B
Appendix B. Calculation of Quality Factor Q
The performance of an optical communication system is often characterized using the
bit error rate (BER). However the BER measurement for high performance
transmission link can be extremely difficult. For example, when requiring a BER of
1×10-15 a minimum measurement time of 27 hours is required at 10Gb/s data rate. In
these circumstances, Q factor measurement has become the new quality evaluation
parameter.
System Q factor adopts the concept of S/N ratio in a digital signal and is an evaluation
method that assumes a normal noise distribution. It is defined as:
Q=
µ1 − µ 0
σ1 + σ 0
Equation B.1
where µ1 and µ0 correspond to the levels of the transmitted data ‘1’s and ‘0’s, and σ1
and σ0 correspond to the standard deviation of the noise on ‘1’s and ‘0’s respectively.
The BER is related to Q as follows:
2
1
⎛ Q ⎞ exp(−Q / 2)
BER = erfc⎜
≈
⎟
2
Q 2π
⎝ 2⎠
Equation B.2
This relationship between BER and Q is further illustrated in figureB.1. As can be
seen from the figure, the minimum value of Q that will enable an error-free system is
6. Usually much higher values of Q would be expected of a practical system.
log(BER)
Figure B.1 Relationship between Q and BER
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-13
-14
-15
-16
0
1
2
3
4
Q (linear units)
73
5
6
7
8
```
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