Optical Bit Error Rate

Chapter 9 - Error Detection and Correction Codes

9.1   INTRODUCTION

Binary communications opened the road to many innovations in both implementation
and theory. One of them was error detection and correction codes. But, what
does this really mean to communications?

We answer this question with an example. Consider a channel that requires an
expected bit error rate performance of 10–5, or a single error in 100,000 bits received,
at a bit rate of 2 Mbit/s and a maximum line length of 2 km. At this rate,
100,000 bits are received within 50 ms, and thus it is expected that there will be on
average one error every 50 ms, or 20 errors per second.

Clearly, if we elongate the line length to four kilometers and keep the same rate,
then because of attenuation and more noise added to the signal, the BER is expected
to increase. For the sake of argument, let us assume that if we double the line
length, then BER increases to 10–2, or a single error every 100 bits received. Then,
at 2 Mbit/s, there are expected to be on average one error every 50 μs, or 20,000 errors
per second.

Now, assume that the signal includes an error detection and correction code such
that on average it corrects one error every 200 bits received; that is, it corrects one
error every 50 μs, or 20,000 errors per second. Such a code would have corrected
all expected errors and made the 4 km line length errorless and possible to use.
However, because the EDC adds approximately 10% of overhead to the original 2
Mbit/s signal, the line rate now becomes 2.2 Mbit/s, and this rate increase brings the
BER to the original 10–5. Similar calculations and arguments are also used for bit
rates at 10 Gbit/s and 10–12 BER, when the fiber length needs to be increased from
60 km to 200 km.

As a consequence, efficient error correction “coding” allows for longer distances
between transmitter and receiver, for lower transmitted power and weaker received
signals, and for communication in noisy environments. Therefore, communications
standards define the type of error detection and correction code to be used as well as
the strategy that is best suited to the particular transmission applications.

The impact of FEC codes on reach for optical signals is simulated in one of the
exercises using the CD-ROM that accompanies this book (see Appendix B for a de-
scription of these exercises).

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