crc32 - how to correct single bit error with CRC?

Question

If we are sure that we are in "single error" mode , how we can correct that error using CRC gotten and CRC expected? i know how to detect errors but how to correct?

question from:https://stackoverflow.com/questions/66068166/how-to-correct-single-bit-error-with-crc

Answer 1

Depending on the number of bits in a message (data + crc), and the CRC polynomial, a single bit error can be corrected. In order for this to work, every single bit error would have to produce a unique CRC. If there are any duplicates, it won't work, but a different CRC polynomial might solve the issue.

If the number of bits is not too large, a table can be used. Each entry in the table would contain a CRC and the bit index of the error. The table can be sorted by CRC so that a binary search can be used.

Another option is to compute the CRC, then reverse cycle the CRC until only the least significant bit is 1 while the rest are 0. This can be expanded to handle single burst correction, reverse cycling the CRC until more than half of the most significant bits are 0, depending on the CRC and message length.

http://www2.hawaii.edu/~tmandel/papers/CRCBurst.pdf

CRCBurst.pdf's algorithm is similar to reverse cycling a CRC, except it requires the least significant bit to be 1, which is an issue for a short burst at the beginning of a message, but if using reverse cycling, the CRC can be backwards cycled until least significant bit is 1, and the leading bits of the CRC that correspond to bits that would precede the message are ignored.

There is a 32 bit CRC that can correct up to 3 error bits for a message with 1024 bits (992 data, 32 CRC), but the table is huge (1.4 GB):

https://stackoverflow.com/a/62201417/3282056

Link to example code:

https://github.com/jeffareid/misc/blob/master/crccor3.c

An error correcting BCH code could be used for 992 bits of data and 30 parity bits for 3 error bit correction.