Digital Signal Processing Reference
In-Depth Information
a
b
Forward recursion
a
0
1
2
y
c1
y
u
MAP 1
3
L
1
L
1
4
∏
−
1
∏
∏
5
L
2
L
2
u
k
=
0
6
y
c2
MAP 2
u
k
=
1
7
s
k
s
k
+1
s
k
+2
s
k
+3
s
k
+4
u
k
,
c
k
Backward recursion
β
Fig. 20
Basic structure of an iterative Turbo decoder.
(a)
Iterative decoding based on two MAP
decoders.
(b)
Forward/backward recursion on trellis diagram
a
b
γ0
α0
LUT
γ0
+
α
0
0
α0
State
m
−
+
α
0
1
+
α1
α1
γ1
γ1
Fig. 21
ACSA structure.
(a)
Flow of state metric update.
(b)
Circuit implementation of an
ACSA unit
max
β
k
(
s
k
)=
s
k
+
1
{
β
k
+
1
(
s
k
+
1
)+
γ
k
(
s
k
,
s
k
+
1
)
}.
(14)
The
γ
k
term above is the branch transition probability that depends on the trellis
diagram, and is usually referred to as a branch metric. The max star operator
employed in the above descriptions is the core arithmetic computation that is
required by the MAP decoding. It is defined as:
max
e
−|
a
−
b
|
)
.
e
a
e
b
(
a
,
b
)=
log
(
+
)=
max
(
a
,
b
)+
log
(
1
+
(15)
one step of the trellis per cycle and is often referred to as Radix-2 ACSA unit.
