參數(shù)資料
型號(hào)： AN2407
廠商： 飛思卡爾半導(dǎo)體(中國(guó))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(shí)例
文件頁(yè)數(shù)： 5/48頁(yè)
文件大小： 306K
代理商： AN2407
Theory
Reed Solomon Encoder/Decoder on the StarCore SC140/SC1400 Cores, With Extended Examples, Rev. 1
Freescale Semiconductor
5
where
class
GF(2
m
)
possess
2
m
elements, where
m
is the symbol size, that is, the size of an element, in bits. For example,
in ADSL systems, the Galois field is
GF(256)
. It is generated by the following primitive polynomial:
, can produce 2
m–1
field elements (excluding the zero element). In general, extended Galois fields of
1+x
2
+x
3
+x
4
+x
8
This is a degree-eight irreducible polynomial. The field elements are degree-seven polynomials. Due to the one-to-
one mapping that exists between polynomials over
GF(2)
and binary numbers, the field elements are representable
as binary numbers of eight bits each, that is, as bytes. In
GF(2
m
)
fields, all elements besides the zero element can be
represented in two alternative ways:
1.
In binary form, as an ordinary binary number.
2.
In exponential form, as
α
p
. It follows from these definitions that the exponent
p
is an integer ranging
from 0 to (2
m
–2). Conventionally, the primitive element is chosen as 0x02, in binary representation.
As for
GF(2)
, addition over
GF(2
m
)
is the bitwise XOR of two elements. Galois multiplication
is performed in two
steps: multiplying the two operands represented as polynomials and taking the remainder of the division by the
primitive polynomial, all over
GF(2)
. Alternatively, multiplication can be performed by adding the exponents of
the two operands. The exponent of the product is the sum of exponents, modulo 2
m
–1.
Polynomials over the Galois field are of cardinal importance in the Reed-Solomon algorithm. The mapping
between bitstreams and polynomials for
GF(2
m
)
is analogous to that of
GF(2)
. A polynomial of degree
D
over
GF(2
m
)
has the most general form:
where the coefficients
f
0
–
f
D
are elements of
GF(2
m
)
. A bitstream of
(N+
1
)m
bits
is mapped into an abstract
polynomial of degree
N
by
setting the coefficients equal to the symbol values and the exponents of
x
equal to the bit
locations. The Galois field is
GF(256)
, so the bitstream is divided into symbols of eight
consecutive bits each. The
first symbol in the bitstream is 00000001. In exponential representation, 00000001 becomes
α
0
.
Thus,
α
0
becomes
the coefficient of
x
0
.
The second symbol is 11001100, so the coefficient of
x
is
α
127
and so on.
The elements are conventionally arranged in a log table so that the index equals the exponent, and the entry equals
the element in its binary form.
Table 1
displays the log table for ADSL systems.
Table 1.
Exponential-to-Binary Table for ADSL Systems
p
α
p
0
1
2
3
4
0x01
0x02
0x04
0x08
0x10
i
N
∈
f x
( )
f
0
f
1
x
f
2
x
2
f
3
x
3
…
f
+
D
x
D
+
+
+
=
11110011
11111101
10110111
01110101
11001100
00000001
α
233
α
80
α
158
α
21
α
127
α
0
f(x) =
α
0
+
α
127
x
+
α
21
x
2
+
α
158
x
3
+
α
80
x
4
+
α
233
x
5
...
相關(guān)PDF資料
PDF描述
AN2410S Video Camera Circuit
AN2441S Color Encoder Circuit
AN246 Transmission lines and terminations with Philips Advanced Logic families
AN2510S Video Camera Circuit
AN2512S Video Camera Circuit
相關(guān)代理商/技術(shù)參數(shù)
參數(shù)描述
AN2407FHP 制造商:Panasonic Industrial Company 功能描述:IC
AN241 制造商:Panasonic Industrial Company 功能描述:IC
AN2410S 制造商:未知廠家 制造商全稱:未知廠家 功能描述:Video Camera Circuit
AN2416 制造商:VYNCKIER ENCLOSURE SYSTEMS 功能描述:ENCLOSURE, JUNCTION BOX, POLYESTER BEIGE; Enclosure Type:Junction Box; Enclosure Material:Fiberglass Reinforced Polyester; Body Color:Beige; External Height - Imperial:24.21"; External Height - Metric:615mm; IP Rating:IP66 ;RoHS Compliant: Yes
AN2416PL 制造商:VYNCKIER ENCLOSURE SYSTEMS 功能描述:ENCLOSURE, JUNCTION BOX, POLYESTER BEIGE; Enclosure Type:Junction Box; Enclosure Material:Fiberglass Reinforced Polyester; Body Color:Beige; External Height - Imperial:24.21"; External Height - Metric:615mm; IP Rating:IP66 ;RoHS Compliant: Yes
發(fā)布緊急采購(gòu)，3分鐘左右您將得到回復(fù)。

采購(gòu)需求

(若只采購(gòu)一條型號(hào)，填寫一行即可)

發(fā)布成功！您可以繼續(xù)發(fā)布采購(gòu)。也可以進(jìn)入我的后臺(tái)，查看報(bào)價(jià)

發(fā)布成功！您可以繼續(xù)發(fā)布采購(gòu)。也可以進(jìn)入我的后臺(tái)，查看報(bào)價(jià)

*型號(hào) *數(shù)量 廠商 批號(hào) 封裝
添加更多采購(gòu)

我的聯(lián)系方式

*
*
*