L64704 LSI Logic Corporation, L64704 Datasheet - Page 160

• Manufacturer Part Number: L64704
• Description: Satellite Decoder Technical Manual 5/97
• Manufacturer: LSI Logic Corporation

7-16
x
errors. The original message can be precisely reconstructed from the
check symbols, as long as the number of errors in the code word is less
than or equal to
7.3.1.2 Reed-Solomon Correction Codes
Reed-Solomon (RS) error correction codes are systematic and operate
on bytes rather than single-bit data streams. They are especially good in
burst error applications. The importance of RS codes is illustrated by
their adoption as international and domestic standards in various areas
of applications. The codes are expressed by convention as two numbers,
the first indicating the total codeword length (N), and the second indicat-
ing the number of message bytes (K). The difference between these two
numbers (N – K) is the number of check bytes. A (255, 233) RS code,
for instance, with eight-bit bytes, was adopted as part of the standard for
space missions by both the European Space Agency and NASA. The
compact disc digital-audio system uses a combination of a (32, 28) RS
code and a (28, 24) RS code. The MIL-STD-2179/ANSI X3B.6 media
exchange standard uses a (161, 153) RS code and a (128, 118) RS code
for high-density magnetic recording.
The L64704 uses the following generator polynomial for RS codes:
where a is a root of the binary primitive polynomial:
A data byte (d
d
The error correcting power of an RS code is related to the number of
redundant check symbols in its code words. In general, an RS code with
2T check symbols per code word can correct up to T byte errors per
code word. Higher redundancy allows more errors to be corrected
The remainder of this section describes the process of correcting trans-
mission errors with Reed-Solomon codes.
The FEC Decoder Pipeline
R 1
i
8
7
=
–
a
+
0
7
x
+ d
x
4
+
+
6
a
x
6
i
3
+ .... + d
+
x
7
, d
2
R 2
+
6
1
, .... d
1
a + d
.
1
, d
0
in GF(256), the finite field with 256 elements.
0
) is identified with the element