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62 Xilinx Development System
Xilinx System Generator v2.1 Reference Guide
♦ IESS-308 (208): implements IESS-308 specification (208, 192) shortened RS
code.
♦ IESS-308 (219): implements IESS-308 specification (219, 201) shortened RS
code.
♦ IESS-308 (225): implements IESS-308 specification (225, 205) shortened RS
code.
• Symbol Width: specifies the symbol width for the RS code. The RS decoder
supports symbol width from 3 to 12.
• n: specifies the length of the RS code. The RS decoder supports code with length
from (2
sw
-1) to 3, where sw is symbol width.
• k: specifies the number of information symbols in a RS code. The RS decoder
supports code with length from (n-2) to max((n-128), 1).
• Field Polynomial: specifies the field polynomial used to generate the Galois field
for the code. It is entered as an binary array where the 1st element corresponds to
the highest degree of the polynomial. A value of zero causes the default
polynomial for the given symbol width to be selected. The specified polynomial
should be a primitive polynomial for the given symbol width. The default
polynomials for the specified symbol width are:
• Generator Start: specifies the Galois field logarithm of the first root of the
generator polynomial g(x), i.e.:
where
a = a primitive root of the Galois field for the code
GS = Generator Start
h = Scaling Factor. Normally, Generator_Start is 0 or 1; however, it can be any non-
negative integer between 0 and (2
16
- 1).
Symbol Width Default Polynomials Array Representation
3x
3
+ x + 1 [1 0 1 1]
4x
4
+ x + 1 [1 0 0 1 1]
5x
5
+ x
2
+ 1 [1 0 0 0 1 1]
6x
6
+ x + 1 [1 0 0 0 0 1 1]
7x
7
+ x
3
+ 1 [1 0 0 0 1 0 0 1]
8x
8
+ x
4
+ x
3
+ x
2
+ 1 [1 0 0 0 1 1 1 0 1]
9x
9
+ x
4
+ 1 [1 0 0 0 0 1 0 0 0 1]
10 x
10
+ x
3
+ 1 [1 0 0 0 0 0 0 1 0 0 1]
11 x
11
+ x
2
+ 1 [1 0 0 0 0 0 0 0 0 1 0 1]
12
x
12
+ x
6
+ x
4
+ x + 1
[1 0 0 0 0 0 1 0 1 0 0 1 1]
gx() xa
hx GS i+()
–()
i 0=
nk–1–
∏
=