Digital Signal Processing Reference
In-Depth Information
in which the resulting
T
(
m
)
i
(
d
i
) is scaled so that evaluations sum to one:
i
(
1)
þT
(
m
i
(
þ
1)
¼
1 for each
i
. (The term pseudo posterior is employed
since the pseudo priors
U
(
m
i
(
d
i
) are not generally the true
a priori
probabilities.)
3. De-interleave the extrinsic probabilities from the inner decoder
T
(
m
)
T
(
m
)
j
(
c
j
¼
0)
¼ T
(
m
)
(
d
i
¼þ
1),
i
T
(
m
)
j
(
c
j
¼
1)
¼ T
(
m
)
(
d
i
¼
1), with
j ¼P
(
i
)
i
for
i ¼
1, 2,
...
,
N
, which variables will replace the channel likelihood values in
the outer decoder.
4. Calculate the pseudo-posteriors from the outer encoder as
(
c
j
)
X
c
i
,
i
=
j
f
(
c
)
Y
l
=
i
[Pr(
c
j
jd
)]
(
m
)
/ T
(
m
)
j
T
(
m
l
(
c
l
)
|
{z
}
/U
(
mþ
1)
j
(
c
j
)
in which
U
(
mþ
1)
j
(
c
j
) is scaled so that evaluations sum to one
U
(
mþ
1)
j
(0)
þU
(
mþ
1)
j
(1)
¼
1
for all
j:
The pseudo posteriors Pr(
c
j
jd
) should likewise be scaled such that
Pr(
c
j
¼
0
jd
)
þ
Pr(
c
j
¼
1
jd
)
¼
1,
for all
j:
5. Interleave the extrinsic probabilities from the outer encoder as
U
(
mþ
1)
i
(
d
i
¼þ
1)
¼ U
(
mþ
1)
j
(
c
j
¼
0),
U
(
mþ
1)
i
(
d
i
¼
1)
¼ U
(
mþ
1)
(
c
j
¼
1), with
j ¼P
(
i
)
j
for
i ¼
1, 2,
...
,
N
, which variables will replace the priors in the inner decoder.
Increment the iteration counter to
mþ
1, and return to step 2.
The algorithm iterates until convergence is observed, or a maximum number of iter-
ations is reached. Before detailing the inner workings of steps 2 and 4 in Section 3.5,
we recall some basic properties applicable to this scheme.
3.4.1 Basic Properties of Iterative Decoding
Observe first from steps 2 and 4 in the previous section, that the pseudo posterior
marginals from either decoder are
[Pr(
d
i
jy
)]
(
m
)
/ U
(
m
)
i
(
d
i
)
T
(
m
)
(
d
i
)
i
/ U
(
mþ
1)
j
(
c
j
)
T
(
m
)
j
[Pr(
c
j
jd
)]
(
m
)
(
c
j
), with
j ¼P
(
i
) and
d
i
¼
(
1)
c
j
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