Using this Log MAP decoder and two component codes, we can create a R1/2, K5 turbo code
with random interleaver of size 65,536. The simulated BER performance as a function of Eb/No is
shown in Fig. 5.48.
PERFORMANCE IMPROVEMENT TECHNIQUES 261
R = 1/2, K = 5, Turbo Decoder Performance
1.E??“07
1.E??“06
1.E??“05
1.E??“04
1.E??“03
1.E??“02
1.E??“01
0 1 2 3 4 5 6 7 8 9 10 11
Eb/No (dB)
BER
2
3
18
6
FIGURE 5.48 Turbo decoder BER performance in AWGN.
Here we notice a few interesting observations: specifically as the number of iterations increases,
the BER performance improves. Also the incremental improvement decreases with each additional
iteration increment. Lastly, we see an error floor or asymptote beginning to take form at least for BER
1E-5 at an Eb/No of approximately 0.7 dB. Lastly, for this BER, there is a coding gain of approximately
9 dB. This asymptote behavior can be expressed using the following approximation [29].
(5.84)
where Dfree is the average number of ones on the minimum free distance, R is the code rate, dfree is the
code minimum free distance (this depends on the interleaver and generator polynomials). This bound
determines the code performance at high SNR.
As one can see from the turbo decoder??™s performance (see Fig.
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