L64724 LSI Logic Corporation, L64724 Datasheet - Page 183

• Manufacturer Part Number: L64724
• Description: Satellite Receiver
• Manufacturer: LSI Logic Corporation

7.3.1.3 Error Handling and Correction
applications. The codes are expressed by convention as two numbers,
the first indicating the total codeword length (N), and the second
indicating 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 8-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 L64724 uses the following generator polynomial for RS codes:
where
A data byte (d
d
elements.
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
two T 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
transmission errors with Reed-Solomon codes.
A bit error occurs when a transmitted zero is received as a one or vice
versa. A byte error occurs when one or more bits in the byte have errors.
For example, a byte with only one bit error is counted as one byte error,
and a byte with m bit errors (all bits are inverted) is also counted as one
byte error. As long as a code word has no more than T =
errors, the RS Decoder corrects all errors. When a code word has more
than T =
excessive errors and asserts the ERROROUTn signal to notify the user.
Reed-Solomon Decoder
7
R
x
7
i
=
8
+ d
–
0
+
1
x
6
x
is a root of the binary primitive polynomial:
4
+
6
+
R
+ .... + d
x
i
7
3
, d
2
+
x
6
, .... d
2
byte errors, the RS decoder detects the presence of
+
1
1
+ d
1
, d
0
0
) is identified with the element
in GF(256), the finite field with 256
R
2
byte
7-13