Cryptography Reference
In-Depth Information
The main difference with the previous scheme thus lies in the implementation of
the SISO equalizer and SISO decoder. Indeed, these latter no longer exchange
probabilistic information at binary level but at symbol level, whether in LLR
form or directly in probability form. The interested reader can find further
details on this subject in [11.8], for example.
Figure 11.10 - Baseband model of traditional coded modulation systems.
As a general rule, the channel code is a convolutional code and the chan-
nel decoder uses a soft-input soft-output decoding algorithm of the MAP type
(or its derivatives in the logarithmic domain: Log-MAP and Max-Log-MAP).
Again, we will not consider the hardware implementation of the decoder since
this subject is dealt with in Chapter 7. Note, however, that unlike classical
turbo decoding schemes, the channel decoder here does not provide extrinsic
information on the information bits, but instead on the coded bits.
On the other hand, we distinguish different optimization criteria to imple-
ment the SISO equalizer, leading to distinct families of turbo equalizers. The
first, sometimes called "turbo detection" and what we call MAP turbo equal-
ization here, uses an equalizer that is optimal in the Maximum
A Posteriori
sense. The SISO equalizer is then typically performed thanks to the BCJR-
MAP algorithm. As we shall see in the following section, this approach leads
to excellent performance, but like the classical MLSD equalizer, it has a very
high computation cost which excludes any practical implementation in the case
of modulations with a large number of states and for transmissions on channels
having large time delays. We must then turn towards alternative solutions, with
less complexity but that will necessarily be sub-optimal in nature. One strategy
that can be envisaged in this context involves reducing the number of branches
to examine at each instant in the trellis. This approach is commonly called
"reduced complexity MAP turbo equalization". We know different methods to
reach this result, which will be briefly presented in the following section. An-
other solution is inspired by classical equalization methods and implements an
optimized SISO equalizer following the minimum mean square error (MMSE)
criterion. We thus obtain an MMSE (filtering-based) turbo equalizer, a scheme
described in Section 11.1.6 and that appears as a very promising solution today
for high data rates transmissions on highly frequency-selective channels.
