Xilinx V2.1 manual g x = ∏ x –ahxGS + i i =, Xilinx System Generator v2.1 Reference Guide

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 (2sw -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:

Symbol Width	Default Polynomials	Array Representation
3	x3 + x + 1	[1 0 1 1]
4	x4 + x + 1	[1 0 0 1 1]
5	x5 + x2 + 1	[1 0 0 0 1 1]
6	x6 + x + 1	[1 0 0 0 0 1 1]
7	x7 + x3 + 1	[1 0 0 0 1 0 0 1]
8	x8 + x4 + x3 + x2 + 1	[1 0 0 0 1 1 1 0 1]
9	x9 + x4+ 1	[1 0 0 0 0 1 0 0 0 1]
10	x10 + x3 + 1	[1 0 0 0 0 0 0 1 0 0 1]
11	x11 + x2 + 1	[1 0 0 0 0 0 0 0 0 1 0 1]
12	x12 + x6 + x4 + x + 1	[1 0 0 0 0 0 1 0 1 0 0 1 1]

∙Generator Start: specifies the Galois field logarithm of the first root of the generator polynomial g(x), i.e.:

n –k – 1

g( x) = ∏ ( x –ahx(GS+ i) ) i = 0

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 (216 - 1).

62 Xilinx Development System