Cryptography Reference
In-Depth Information
Figure 10.3 - Binary error rate (BER) as a function of the signal to noise ratio E
b
/N
0
of the 8-PSK TTCM with 8 states using the RSC code of Figure 10.2(a). Transmis-
sion over a Gaussian channel. Spectral eciency
η
=2
bit/s/Hz. Blocks of 10,000
information bits, 5,000 modulated symbols. MAP decoding algorithm. Curves taken
from [10.6].
atic. On the other hand, this technique uses interleaving at bit level, and not at
symbol level like in the previous approach.
The criterion for optimizing the TTCM proposed in [10.1] is based on maxi-
mizing the
effective Euclidean distance
, defined as the minimum Euclidean dis-
tance between two encoded sequences whose information sequences have a Ham-
ming weight equal to 2. Figures 10.5 and 10.6 show two examples of TTCMs
built on this principle.
The correction performance of these two TTCMs over a Gaussian channel
are presented in Figures 10.7 and 10.8. At high and average error rates, they are
close to those given by the scheme of Robertson and Wörz; on the other hand,
using interleavers operating on the bits rather than on the symbols has made it
possible to significantly improve the behaviour at low error rates.
TTCMs lead to excellent correction performance over a Gaussian channel,
since they are an
ad hoc
approach to turbo coded modulation. However, they
have the main drawback of very limited flexibility: a new code must be defined
for each coding rate and each modulation considered. This drawback is cumber-
some in any practical system requiring a certain degree of adaptability. On the
other hand, although they are a quasi-optimal solution to the problem of coded
modulations for the Gaussian channel, their behaviour over fading channels like
Rayleigh channels leads to mediocre performance [10.9].
