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See Hamming code for an example of an error-correcting code. Parity bit checking is used occasionally for transmitting ASCII characters, which have 7 bits, leaving the 8th bit as a parity bit. For example, the parity bit can be computed as follows. Assume Alice and Bob are communicating and Alice wants to send Bob the simple 4-bit message 1001.
A parity bit is a bit that is added to a group of source bits to ensure that the number of set bits (i.e., bits with value 1) in the outcome is even or odd. It is a very simple scheme that can be used to detect single or any other odd number (i.e., three, five, etc.) of errors in the output.
Since the source is only 4 bits then there are only 16 possible transmitted words. Included is the eight-bit value if an extra parity bit is used (see Hamming(7,4) code with an additional parity bit). (The data bits are shown in blue; the parity bits are shown in red; and the extra parity bit shown in green.)
The parity bit may be used within another constituent code. In an example using the DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits.
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The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number n of bits, and then computes the bitwise exclusive or (XOR) of all those words. The result is appended to the message as an extra word.
A multidimensional parity-check code (MDPC) is a type of error-correcting code that generalizes two-dimensional parity checks to higher dimensions. It was developed as an extension of simple parity check methods used in magnetic recording systems and radiation-hardened memory designs .
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