B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

Figure 14.3
Performance
comparison of
coded (doshed)
and uncoded
(solid) systems.
14.5 The Effects of Error Correction 825
--- Uncoded
----- Coded
.... .... .... ..... .... ' '' ...''' ' ''''''''' ' ''''' ' ' ' '
\
\
\
\
\
\
\
\
1 0 ~7 -------------------'-
2 4 8 1 0 12
It should be noted that the coded system performance of Fig. 14.3 is in fact a slightly
optimistic approximation. The reason is that in analyzing its bit error rate, we assumed that
the decoder will not take any action when the number of errors in each codeword exceeds t.
In practice, the decoder never knows how many errors are in a codeword. Thus, the decoder
will always attempt to correct the codeword, assuming that there are no more than t bit errors.
This means that when there are more than t bit errors, the decoding process may even increase
the number of errors. This counterproductive decoding effect is more likely when P e is high
at low E b /N. This effect will be shown later in Sec. 14.13 as a MATLAB exercise.
Example 14.6 Compare the performance of an AWGN BSC using a single-error correcting (15, 11) code
with that of the same system using uncoded transmission, given that E b / N = 9.0946 for the
uncoded scheme and coherent PSK is used to transmit the data.
From Eq. (14.31b),
and from Eq. (14.31a),
P eu = Q(✓18.1892) = 1.0 X 10-S
p 14 [ Q
( : (181892))]'
= 14(1.3 X 10- 4 ) 2 = 2.03 X 10-?