Soft decision decoding of a scheduled convolutional code
A method for decoding a predetermined code word is specified in which the code word comprises a number of positions having different values. In this method, encoding is performed, in particular, by way of a terminated convolutional code. Each position of the code word is correlated with a safety measure (soft output) for a most probable Boolean value by performing the correlation on the basis of a trellis representation. The decoding of the code word is determined by the correlation of the individual positions of the code word.
1. A method for decoding a predetermined code word, wherein said code word comprises a number of positions having different values, comprising the steps of:
providing a processor comprising a central processing unit, memory, an input/output interface, and a data bus connecting said central processing unit to said memory and said input/output interface, said processor decoding a predetermined code word;
determining a calculation rule for a soft-output value for each position of said code word, each said position of said code being correlated with said soft-output value, according to the formula
L
(
U
i
y
)
=
ln
(
∑
c
ε
Γ
i
(
+
1
)
exp
(
-
(
y
-
c
)
T
(
y
-
c
)
2
σ
2
)
∑
c
ε
Γ
i
(
-
1
)
exp
(
-
(
y
-
c
)
T
(
y
-
c
)
2
σ
2
)
)
,
for
i
=
1
,
…
,
K
,
where
L(U i |y) is a safety measure (soft output) for the i-th position of the code word to be determined;
y is a demodulation result to be decoded;
c is a code word;
Γ i (±1) are all code words for u i ±1; and
σ 2 is a variance (channel disturbance);
utilizing a characteristic of a convolutional code, in decoding of said code word, for determining said correlation of said individual positions of said code word from which steps follow of determining states in accordance with a shift register operation, and obtaining a trellis representation from these states;
calculating weights μ q q(s), for an arbitrary choice of yεR N , for nodes (s,q) of said trellis representation by evaluating
μ q :S→ ,
s
exp
(
-
1
2
σ
2
∑
j
=
1
n
(
y
n
(
q
-
1
)
+
j
-
C
j
(
s
)
)
2
)
for qε{1, . . . , Q};
determining mappings A m by way of said trellis representation, running through said trellis representation in the natural direction, and calculating the term A m by
A
m
(
s
)
=
μ
m
(
s
)
∑
t
ε
W
(
s
,
V
m
)
□
A
m
-
1
(
t
)
,
for
m
ε
and a starting value
A
0
(
s
)
=
{
1
⋮
for
s
=
s
0
,
0
⋮
else
determining mappings B m by way of said trellis representation, said trellis representation being run through in opposition to a predetermined direction, and calculating the term B m by
B
m
(
s
)
=
μ
Q
-
m
+
1
(
s
)
∑
t
ε
T
(
s
,
V
Q
-
m
+
2
)
B
m
-
1
(
t
)
,
for
1
≤
m
≤
Q
,
where
B
0
(
s
)
=
{
1
⋮
for
s
=
s
0
,
0
⋮
else
is determined for terminating the recursion; and
determining terms A α i by again running through said trellis representation taking into consideration said terms A m and B m already determined, according to a relation
A
α
i
(
y
)
=
∑
s
ε
S
A
i
-
1
(
s
)
∑
t
ε
T
(
s
,
V
j
i
(
a
)
)
B
Q
-
j
+
1
(
t
)
,
where
j
=
⌊
i
-
1
b
⌋
+
1
;
determining K positions of said code word according to
L
(
U
i
y
)
=
ln
(
A
+
1
i
(
y
)
A
-
1
i
(
y
)
)
,
i
=
1
,
…
,
K
.
2. The method as claimed in claim 1 , wherein said convolutional code has binary state transitions, said method further comprising the steps of:
determining mappings A m recursively by the equation
A m ( s )=μ m ( s )( A m−1 ( {circumflex over (T)} (+1 s ))+ A m−i ( {circumflex over (T)} (−1 , s ))), for m ε ;
determining mappings B m recursively by the equation
B m ( s )=μ Q−m+1 ( s )( B m−1 ( T ( s,+ 1))+ B m−1 ( T ( s,− 1))),
for 1≦m≦Q; and
determining terms A α i , iε{1, . . . , K}, αε{±1} according to the equation
A
α
i
(
y
)
=
∑
s
ε
S
A
i
-
1
(
s
)
B
Q
-
i
+
1
(
T
(
s
,
α
)
)
.
3. The method as claimed in claim 1 , further comprising the step of:
providing a mobile radio network in which said decoding of a predetermined code word operates.
4. The method as claimed in claim 3 , wherein said mobile radio network is a GSM network.
5. The method as claimed in claim 1 , wherein said predetermined code word is a concatenated code word, said method further comprising the steps of:
providing said calculated soft-output values as input data of another decoder.