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Error Correction (1bit and 2 bit):

Error Correction (1 bit)

In error correction, it can say it is an error and it’s over but error correction first we find where the error is and correct the error.

At 1 bit error, the hamming distance between two codes is 2.

# But mind it if there is 1-bit error 0000 it comes at 0001 (and it is invalid because it is not 0000, 0011)

# Same way if there is 1-bit error 0011 it can come at 0001 (Invalid)

So, here we understand the code (0001) is invalid. So, it is an error but not recognized from where the error come from either 0000 or 0011. So, it has confusion.

So, because of receiver can’t understand form the data come from (it has confusion)

So, it can’t correct it.

Therefore, to correct it,

So, both 0000 and 0011 not land on the same code after a 1-bit error.

It should be land in a different code after a 1-bit error.

So, if the receiver got 0001, it knows it is an invalid code, so, it is an error and 0001 is nearest to 0000, so, receiver understands that error is coming from 0000.

So, in this case, if the hamming distance of two valid codes is at least 3 (three), then we can do a single (1) bit error correction for 2-bit error correction.

2-bit error correction: 2-bit error correction means it correct one (1) bit error as well as 2-bit error correction that is maximum of two (2) bit error correction.

2-bit Error Correction:

Same thing as 1 bit 2 valid codes do not overlap after a 2-bit error. So, to correct a 2-bit error the minimum distance between two valid codes is at least 5.