Is it possible to do rudimentary error correction with CRC?

Question

I know the whole intention of using CRC is to do error detection, but I heard someone state that it can be used to do basic error correction in addition to error detection. I was curious if this was the case, and if so, how powerful is it? I mean, we usually refer to CRC as capable of performing x-bit detection, but I'm curious if it is capable of performing x-bit correction. If so, how does this work? Thanks.

Answer 1

It is possible to do single-bit error correction with a CRC. Assume one has a CRC "register" and has functions to run the CRC algorithm forward and backward a bit at a time, ignoring incoming data

int crc_forward(int old_value, int data_bit)
{
  if (old_value & 0x8000)
    return ((old_value ^ 0x8000) SHL 1) ^ 0x1021 ^ data_bit;
  else
    return (old_value SHL 1) ^ data_bit;
}

int crc_reverse(int old_value)
{
  if (old_value & 1)
    return (old_value SHR 1) ^ 0x8810;
  else
    return old_value SHR 1;
}

Suppose one has a packet which is computed so that initializing the crc to some value and running crc_forward for each bit (MSB first) should yield zero. If one gets a CRC value other than zero, one can run the algorithm in reverse (ignoring data bits) until the computed CRC value is 1. That's the location of the incorrect bit.

Note that this approach may be adequate for software error correction in things like NAND flash. To usefully employ it for hardware error correction, one would have to either be able to delay read operations until the ECC could be processed, or else one would need a table of 'syndrome' values and bit positions.