Cryptography Reference
In-Depth Information
called an
EXtrinsic Information Transfer
(EXIT) chart. To elaborate the EXIT
chart, it is necessary to know the transfer characteristics of the extrinsic infor-
mation of each SISO decoder used in the decoding. This section shows how
to establish the transfer function of the extrinsic information for a SISO de-
coder, then construct the EXIT chart, and finally analyse the convergence of
the iterative decoder.
Figure 7.25 - Variation of variance
σ
z
as a function of the the mutual information IA
Transfer function for a SISO decoder of extrinsic information
a. Definition of the mutual information (MI)
If the weighted extrinsic information
z
on the coded binary element
x
∈{−
1
,
+1
x
)
,theMI
I
(
z, x
)
measures
the quantity of information provided on average by
z
on
x
and equals
}
follows a conditional probability density
f
(
z
|
log
2
dz
+
∞
I
(
z, x
)=
1
2
2
f
(
z
|
x
)
f
(
z
|
x
)
×
(7.59)
f
(
z
|−
1
)+
f
(
z
|
+1)
x
=
−
1
,
+1
−∞
