Cryptography Reference
In-Depth Information
of. At each decoding instant, the elementary decoders thus exchange
2
q
values
of extrinsic information.
Figure 10.2 provides two examples of elementary RSC codes used in [10.5,
10.6] to build an 8-PSK TTCM with 8 states of spectral eciency
η
=2
bit/s/Hz
and a 16-QAM TTCM with spectral eciency
η
=3
bit/s/Hz.
(a)
(b)
Figure 10.2 - Examples of elementary RSC codes used in [10.5, 10.6] for the construc-
tion of a 8-PSK turbo trellis (a) and a 16-QAM turbo trellis (b) coded modulations.
Figures 10.3 and 10.4 show the performance of these two TTCMs in terms of
binary error rates (BER) as a function of the signal to noise ratio for transmission
over a Gaussian channel. At high and average error rates, these schemes show
correction performance close to capacity: a BER of
10
−
4
is reached at around
0.65 dB from Shannon's theoretical limit for the transmission of packets of 5,000
coded modulated symbols. On the other hand, as the interleaving function of
the TTCM has not been the object of any particular optimization in [10.5, 10.6],
the error rates curves presented reveal early changes in slope (BER
∼
10
−
5
)that
are very pronounced.
A variant of this technique, proposed by Benedetto
et al.
[10.1] made it pos-
sible to improve its asymptotic performance. An alternative method to build a
TTCM with spectral eciency
q
bit/s/Hz involves using two RSC codes with
rate
q/
(
q
+1)
and for each of them to puncture
q/
2
information bits (
q
is as-
sumed to be even). For each elementary code we thus transmit only half the
information bits and all the redundancy bits. The bits at the output of each
encoder are associated with a modulation with
2
(
q/
2)+1
points. The same oper-
ation is performed for the two RSC codes, taking care that each systematic bit
is transmitted once and only once, so that the resulting turbo code is system-
