5.15.
Let us discuss the FEC encoder in more detail. Recall the generator matrix for a BCH (7,4) code
word was given as
(5.17) G D1 0 1 1 0 0 0
1 1 1 0 1 0 0
1 1 0 0 0 1 0
0 1 1 0 0 0 1 T
G D1 0 1 1 0 0 0
1 1 1 0 1 0 0
1 1 0 0 0 1 0
0 1 1 0 0 0 1 T [P I4]
We wish to discuss how the generator matrix was created. Much work has been done to search for
generator polynomials that produce good results. We will simply refer the reader to widely published
tables that list generator polynomials for various encoders. For example consider Table 5.1 as a starting
point [7].
234 CHAPTER FIVE
TABLE 5.1 BCH Primitive Polynomials
n k G(x) G(x) octal t
7 4 X3 X 1 13 1
15 11 X4 X 1 23 1
32 26 X5 X21 45 1
63 57 X6 X 1 103 1
127 120 X7 X 1 211 1
255 247 X8 X4 X3 X2 1 435 1
These generator polynomials will be used as encoding rules governing the operations of the FEC
encoder. A note to make here is that the generator polynomials listed in Table 5.1 are primitive
polynomials.
The generator polynomial for (7,4) code is given as g(x) x3 x 1 and in binary field this is
represented as
(5.18)
We can create code words by performing cyclic shifting of the generator polynomial as follows:
(5.
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