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HELP AND INFORMATION
BURST ERROR DETECTION
The purpose of this page is to provide an introduction to burst error detection.
Also a burst error detection simulator is provided.
Definitions:
k -> number of bits in the codeword
n -> number of bits in the message
t -> burst length
In order to detect burst errors of length "t" a code word is generated by appending "t" parity bits at the end (or beginning) of the message. The parity bits will be generated by doing an XOR of all of the bits separated by t bits.
Example
t = 3
Message = m
_{1}
m
_{2}
m
_{3}
m
_{4}
m
_{5}
m
_{6}
m
_{7}
m
_{8}
m
_{9}
m
_{10}
n = 10
k = 13
First we pad the message by 0's so the number of bits is divisible by t
New Message = m
_{0}
m
_{1}
m
_{2}
m
_{3}
m
_{4}
m
_{5}
m
_{6}
m
_{7}
m
_{8}
m
_{9}
m
_{10}
m
_{11}
where m
_{0}
and m
_{1}
are filler zeros
New n = 12 (n is now divisible by t)
New k = 15
Parity:
p
_{1}
= m
_{0}
^m
_{3}
^m
_{6}
^m
_{9}
p
_{2}
= m
_{1}
^m
_{4}
^m
_{7}
^m
_{10}
p
_{3}
= m
_{2}
^m
_{5}
^m
_{8}
^m
_{11}
The codeword becomes m
_{0}
m
_{1}
m
_{2}
m
_{3}
m
_{4}
m
_{5}
m
_{6}
m
_{7}
m
_{8}
m
_{9}
m
_{10}
m
_{11}
p
_{1}
p
_{2}
p
_{3}
At the receiving end t equations are used to check the parity of the received codeword.
e
_{1}
= p
_{1}
^(m
_{0}
^m
_{3}
^m
_{6}
^m
_{9}
)
e
_{2}
= p
_{2}
^(m
_{1}
^m
_{4}
^m
_{7}
^m
_{10}
)
e
_{3}
= p
_{3}
^(m
_{2}
^m
_{5}
^m
_{8}
^m
_{11}
)
If any of these equations is not equal to zero, an error has occurred. The number of errors can be obtained by adding e
_{1}
+e
_{2}
+....+e
_{t}
Example:
First provide the length of the burst ("t") you would like to detect
Enter a message word (binary)
The resulting parity bits are
so the codeword is
(You can introduce a burst error smaller or equal to "t" in length, before continuing)
By decoding we get the syndrome
, for a total number of
errors.
Next, you can use simulators for two common burst error detection codes.
These codes can detect burst error of length t which is smaller than or equal to 16
CRC16
Note: All inputs should be in HEX format and include no more than 9 digits
Data Word:
Encoded word:
Remainder:
Fault:
CRC-CCITT
Note: All inputs should be in HEX format and include no more than 9 digits
Data Word:
Encoded word:
Remainder:
Fault: