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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 = m1m2m3m4m5m6m7m8m9m10
n = 10
k = 13

First we pad the message by 0's so the number of bits is divisible by t

New Message = m0m1m2m3m4m5m6m7m8m9m10m11 where m0 and m1 are filler zeros
New n = 12 (n is now divisible by t)
New k = 15

Parity:
p1 = m0^m3^m6^m9
p2 = m1^m4^m7^m10
p3 = m2^m5^m8^m11

The codeword becomes m0m1m2m3m4m5m6m7m8m9m10m11p1p2p3

At the receiving end t equations are used to check the parity of the received codeword.

e1 = p1^(m0^m3^m6^m9)
e2 = p2^(m1^m4^m7^m10)
e3 = p3^(m2^m5^m8^m11)

If any of these equations is not equal to zero, an error has occurred. The number of errors can be obtained by adding e1+e2+....+et

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: