Cryptography Reference
In-Depth Information
We can note that
lim
σ
z
→
0
IA
=0
(the extrinsic information does not provide any
information about datum
x
)andthat
lim
σ
z
→
+
∞
IA
=1
(the extrinsic information
perfectly determines datum
x
).
IA is an increasing monotonous function of
σ
z
; it is therefore invertible. Function
σ
z
=
f
(
IA
)
is shown in Figure 7.25.
Figure 7.27 - (a) Transfer characteristic of the extrinsic information for a 16-state
binary encoder, with rate 2/3 and MAP decoding with different Eb/N0.
(b) EXIT chart and trajectory for the corresponding turbo code, with pseudo-random
interleaving on 20,000 bits, for
E
b
/N
0
=2
dB
.
c. Calculation of the output mutual information
Relation (7.59) allows the calculation of the mutual information IS linked
with the extrinsic information produced by the SISO decoder:
log
2
dz
+
∞
1
2
2
f
s
(
z
|
x
)
IS
=
f
s
(
z
|
x
)
×
(7.62)
f
s
(
z
|−
1
)+
f
s
(
z
|
+1)
x
=
−
1
,
+1
−∞
We can note that IS
∈
[0
,
1]
.
