Cryptography Reference
In-Depth Information
Chapter 10
Turbo codes and large
spectral e
ciency
transmissions
Transporting information in telecommunication systems is carried out at higher
and higher data rates and in narrower and narrower frequency bands. Conse-
quently, we wish to maximize the ratio of the useful data rate to bandwidth,
that is to say, the spectral eciency of the transmissions. To do this, it seems
natural to couple digital modulations having large constellations with powerful
high-rate error correcting codes like turbo codes.
The studies undertaken in this domain are essentially based on two ap-
proaches:
turbo trellis coded modulation
and
pragmatic turbo coded modulation
.
10.1
Turbo trellis coded modulation (TTCM)
Turbo trellis coded modulation or TTCM was introduced by Robertson and
Wörz in 1995 [10.5, 10.6]. It uses the notion of parallel concatenation, which
is at the origin of turbo coding, applied to two trellis coded modulations, or
TCMs.
TCM, introduced by Ungerboeck at the beginning of the 80s [10.7] is based
on the joint optimization of error correction coding and modulation. The coding
is performed directly in the signal space so that the error correcting code and
the bit to signal mapping of the modulation can be represented jointly using
a single trellis. The criterion for optimizing a TCM thus involves maximizing
the minimum Euclidean distance between two coded sequences. To do this,
Ungerboeck proposed a two-step approach: partitioning the constellation of the
modulation into sub-constellations presenting increasing minimum Euclidean
