Hamming Codes (1)
Multiple check bits are employed.
Each check bit is defined over (or covers) a subset of the information bits.
Subsets overlap so that each information bit is in at least two subsets.
dmin is equal to the weight of the minimum-weight nonzero code word.
Hamming Code 1 (Table 1.14)
- dmin = 3, single error correction code.
- Let the set of all code words: C
an error word with single error: ce
the correct code word for the error word: c
then, d(ce,c) = 1 and d(ce, w) > 1 for all other w Î C (see Table 1.15)
- So, a single error can be detected and corrected by finding out the code word which differs in 1 bit position from the error word.