Hamming Codes (3)
- Decoding can be done using the parity-check matrix, H:
(1.28)
- H matrix is can be derived from G matrix.
- An n-tuple c is a code word generated by G if and only if
HcT = 0 (1.29)
- Let d be a data word corresponding to a code word c, which has been corrupted by an error pattern e. Then
d = c + e (1.30)
- Decoding:
- Compute the syndrome, s, of d using H matrix.
- s tells the position of the erroneous bit.