Signal Space Coding over Rings

Chapter 2: Combined coding and modulation techniques 20
d
d
2
free
2
min
Thus, the use of TCM is based on:
(2.17)
• The transmission of dependent sequences of symbols that are mapped into an
expanded constellation of signals; and
• The use of proper expanded constellations.
The generation of dependent sequences is based on the fact that the transmitted signal
s n at the discrete time n depends not only on the corresponding symbol n
on a finite number of previous source symbols [44, 46]:
s
n
n
= f ( a , a
σ = ( a
n
n−1
, a
n−1
n−2
,..., a
,..., a
n−L
)
n−L
These expressions can be given briefly as:
s
σ
n
= f ( a , σ )
n
n
= g(
a , σ )
n+
1 n n
a
n
)
Memory σ n
Figure 2.4 Block diagram of a TCM scheme
Select subset from
constellation
Signal from subset
s n
a , but also
(2.18)
(2.19)