Cryptography Reference
In-Depth Information
Figure 7.14 - Performance in packet error rates (PER) of the UMTS standard turbo
code for
k
= 640
on a Gaussian channel with 4-PSK modulation. Decod-
ing using the Max-Log-MAP algorithm with 6 iterations.
and
R
=1
/
3
Notations
d
k−
1
0
A sequence of data
d
is defined by
d
d
k−
1
)
,where
d
i
is the vector of
m
-binary data applied at the input of the encoder at instant
i
:
d
i
=(
d
i,
1
···
≡
=(
d
0
···
d
i
···
d
i,l
···
d
i,m
)
.Thevalueof
d
i
can also be represented by the scalar
l
=1
m
2
l−
1
d
i,l
, ranging between
0
and
2
m
integer value
j
=
−
1
and we can then
write
d
i
≡
j
.
In the case of two or four-phase PSK modulation (2-PSK, 4-PSK), the en-
coded modulated sequence
u
u
k−
1
0
≡
=(
u
0
···
u
i
···
u
k−
1
)
is made up of vec-
tors
u
i
of size
m
+
m
:
u
i
=(
u
i,
1
···
u
i,l
···
u
i,m
+
m
)
,where
u
i,l
=
±
1
for
l
=
m
+
m
and
m
is the number of redundancy bits added to the
m
bits of
information. The symbol
u
i,l
is therefore representative of a systematic bit for
l
1
···
≤
m
and of a redundancy bit for
l>m
.
The sequence observed at the output of the demodulator is denoted
v
≡
v
k−
1
0
v
i,m
+
m
)
.These iesof
the states of the encoder between instants 0 and
k
is denoted
S
=
S
0
=(
v
0
···
v
i
···
v
k−
1
)
,with
v
i
=(
v
i,
1
···
v
i,l
···
=
(
S
0
···
S
k
)
. The following is based on the results presented in the chapter
on convolutional codes.
S
i
···
