Page 335 - Satellite Communications, Fourth Edition

Chapter
11

Error Control Coding

11.1 Introduction
As shown by Fig. 10.17, the probability of bit error (P ) in a digital trans-
e
mission can be reduced by increasing [E /N ], but there are practical
0
b
limits to this approach. Equation (10.24) shows that for a given bit rate
R ,[E /N ] is directly proportional to [C/N ]. An increase in [C/N ] can
b
0
b
0
0
be achieved by increasing transmitted power and/or reducing the system
noise temperature (to reduce N ). Both these measures are limited by
0
cost and, in the case of the onboard satellite equipment, size. In practi-
4
cal terms, a probability of bit error (P of Eq. 10.18) of about 10 , which
e
is satisfactory for voice transmissions, can be achieved with off the-
shelf equipment. For lower P values such as required for some data,
e
error control coding must be used. Error control performs two func-
tions, error detection and error correction. Most codes can perform both
functions, but not necessarily together. In general, a code is capable of
detecting more errors than it can correct. Where error detection only is
employed, the receiver can request a repeat transmission (a technique
referred to as automatic repeat request, or ARQ). This is only of limited
use in satellite communications because of the long transmission delay
time associated with geostationary satellites, and of course radio and TV
broadcast is essentially one-way so ARQ cannot be employed. What is
termed forward error correction (FEC) allows errors to be corrected
without the need for retransmission, but this is more difficult and costly
to implement than ARQ.
4
A P value of 10 4 represents an average error rate of 1 bit in 10 , and
e
the error performance is sometimes specified as the bit error rate (BER).
It should be recognized, however, that the probability of bit error P e
occurs as a result of noise at the input to the receiver, while the BER is
the actual error rate at the output of the detector. When error control
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