Cryptography Reference
In-Depth Information
Figure 10.8 - BER as a function of the signal to noise ratio
E
b
/
N
0
of the 8-PSK
TTCM with 16 states using the RSC code of Figure 10.6. Transmission over a Gaussian
channel. Spectral eciency
η
=2
bit/s/Hz. 4
×
4,096 information bits. MAP decoding
algorithm. Curves taken from [10.3].
2
erfc
3
1
P
eb
(
s
2
|±
3)
=
σ
√
2
2
erfc
1
1
P
eb
(
s
2
|±
1)
=
σ
√
2
(10.1)
2
erfc
1
2
erfc
5
2
erfc
1
1
1
1
P
eb
(
s
1
|±
3)
=
σ
√
2
−
σ
√
2
≈
σ
√
2
2
erfc
3
+
1
2
erfc
1
2
erfc
1
1
1
σ
√
2
σ
√
2
σ
√
2
P
eb
(
s
1
|±
1)
=
≈
where erfc represents the complementary error function and
σ
2
designates the
noise variance on the channel. We observe that binary position
s
2
is on average
better protected by the modulation than position
s
1
.
Consequently, it is possible to define several strategies for building modula-
tion symbols by associating as a matter of priority the systematic bits or redun-
