Parity Bits

Parity Bits

For example, consider parity: A single parity bit is appended to each data block (e.g. each character in ASCII systems) so that the number of 1 bits always adds up to an even (odd) number.

1000000(1) 1111101(0)

The Hamming Distance for parity is 2, and it cannot correct even single-bit errors (but can detect single-bit errors).

As another example, consider a 10-bit code used to represent 4 possible values: ``00000 00000'', ``00000 11111'', ``11111 00000'', and ``11111 11111''. Its Hamming distance is 5, and we can correct 2 single-bit errors:

For instance, ``10111 00010'' becomes ``11111 00000'' by changing only two bits.

However, if the sender transmits ``11111 00000'' and the receiver sees ``00011 00000'', the receiver will not correct the error properly.

Finally, in this example we are guaranteed to catch all 2-bit errors, but we might do better: if ``00111 00111'' contains 4 single-bit errors, we will reconstruct the block correctly.