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參數(shù)資料
| 型號： | AN2407 |
| 廠商： | 飛思卡爾半導(dǎo)體(中國)有限公司 |
| 英文描述： | Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples |
| 中文描述： | 里德所羅門編碼器/的StarCore SC140/SC1400核心解碼器，以擴(kuò)展實例 |
| 文件頁數(shù)： | 8/48頁 |
| 文件大?。?/td> | 306K |
| 代理商： | AN2407 |
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Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples, Rev. 1
8
Freescale Semiconductor
Theory
where
i
0
, i
1
and so on denote the error location indices, and
ν
the actual number of errors that have
occurred. The
2T
syndromes are obtained by evaluating the received polynomial
r(x)
at the
2T
field
points:
Since
c(x)
is a multiple of
g(x)
, it has the following general form:
where
q(x)
is a message-dependent polynomial. It follows from the definition of
g(x)
that the following
field points:
are roots of
g(x)
. Hence
c(x)
vanishes at the
2T
points and the syndromes:
contain only of the part consisting of the error polynomial
e(x)
:
If all
2T
syndromes vanish,
e(x)
is either identically zero, indicating that no errors have occurred
during the transmission, or an undetectable error pattern has occurred.
If one or more syndromes are
non-zero, errors have been detected. The next steps of the decoder are to retrieve the error locations
and the error values from the syndromes. Denoting the actual number of errors as
ν
,
error values
as
Y
k
, the
2T
syndromes
S
1
–
S
2T
can then be expressed as follows:
e
as
X
k
and the
Thus, there are
2T
equations to solve that are linear in the error values
Y
k
and non-linear in the error
locations
X
k
.
α α
2
α
3
… α
2
T
,
,
··
,
c x
( )
q x
( )
g x
( )
=
α α
2
α
3
… α
2
T
,
,
,
S
1
S
2
S
3
…
S
2
T
,
,
,
S
1
e
α
( )
e
α
2
(
=
S
2
)
=
S
3
…
e
α
3
(
)
=
S
2
T
e
α
2
T
(
)
=
α
i
k
k
S
1
Y
1
X
1
Y
2
X
2
)
2
+
)
3
+
Y
3
X
3
…
Y
ν
X
ν
)
2
Y
3
X
3
+
)
3
Y
3
X
3
+
+
+
=
S
2
Y
1
X
1
(
Y
2
X
2
(
(
)
2
…
Y
ν
X
ν
)
3
…
Y
ν
X
ν
(
)
2
)
3
=
S
3
…
Y
1
X
1
(
Y
2
X
2
(
(
(
=
S
2
T
Y
1
X
1
(
)
2
T
Y
2
X
2
(
)
2
T
Y
3
X
3
(
)
2
T
…
Y
ν
X
ν
(
)
2
T
+
+
=
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