L64704 LSI Logic Corporation, L64704 Datasheet - Page 162

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

7.3.3
Performance
Analysis
Equation 7.3
7-18
The performance of the code against independent random byte errors
can be computed by the equation:
where:
N
p
T
q
When more than T byte errors occur in a code word, the RS Decoders
usually detect the presence of excessive errors and raise the uncorrect-
able error flag to notify the user. However, there is a small probability that
the erroneous decoded code word remains undetected. The undetected
erroneous code word rate is:
For the code format (255, 223), the percentage redundancy of the RS
code is 32/255 = 12.5%. With this modest amount of overhead, the cod-
ing system corrects error bursts of 16 bytes for T = 16.
trates the random error correction capability with a codeword length of
255 when various correction values expressed as T are programmed into
the device.
The FEC Decoder Pipeline
q
----- -
T !
N
1
i
=
---------------- -
2
i
m
=
N
–
T
N
Code word length in bytes
Input byte error rate
Number of errors to correct
Output byte error rate
Binomial coefficient that represents the number of ways of choosing i
items from a collection of N distinct items
1
+
1
T
---- N
N
i
i
=
N
T
i
+
1
p
i
N
i
1 p
–
p
i
N
1 p
–
i –
N
i –
Figure 7.17
illus-