Simple Parity Checking or One-dimension Parity Check

Simple Parity Checking or One-dimension Parity Check

The most common and least expensive mechanism for error- detection is the simple parity check. In this technique, a redundant bit called parity bit, is appended to every data unit so that the number of 1s in the unit (including the parity becomes even).
Blocks of data from the source are subjected to a check bit or Parity bit generator form, where a parity of 1 is added to the block if it contains an odd number of 1’s (ON bits) and 0 is added if it contains an even number of 1’s. At the receiving end the parity bit is computed from the received data bits and compared with the received parity bit. This scheme makes the total number of 1’s even, that is why it is called even parity checking. Considering a 4-bit word, different combinations of the data words and the corresponding code words

Even-parity Checking Scheme

An observation of the table reveals that to move from one code word to another, at least two data bits should be changed. Hence these set of code words are said to have a minimum distance (hamming distance) of 2, which means that a receiver that has knowledge of the code word set can detect all single bit errors in each code word. However, if two errors occur in the code word, it becomes another valid member of the set and the decoder will see only another valid code word and know nothing of the error. Thus errors in more than one bit cannot be detected. In fact it can be shown that a single parity check code can detect only odd number of errors in a code word.