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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.
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.
Linear Network Coding, a type of erasure correcting code across networks instead of point-to-point links; Long code; Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes; LT code, which is a near-optimal rateless erasure correcting code (Fountain code) m of n codes
It is also used in Evolution-Data Optimized and LTE wireless networks. Type I Hybrid ARQ is used in ITU-T G.hn, a high-speed Local area network standard that can operate at data rates up to 1 Gbit/s over existing home wiring (power lines, phone lines and coaxial cables).
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 .
The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code, also known as a Simplex code. The parity-check matrix has the property that any two columns are pairwise linearly independent.
Checksum schemes include parity bits, check digits, and longitudinal redundancy checks. Some checksum schemes, such as the Damm algorithm , the Luhn algorithm , and the Verhoeff algorithm , are specifically designed to detect errors commonly introduced by humans in writing down or remembering identification numbers.
The data must be divided into transmission blocks, to which the additional check data is added. The term usually applies to a single parity bit per bit stream, calculated independently of all the other bit streams . [1] [2] This "extra" LRC word at the end of a block of data is very similar to checksum and cyclic redundancy check (CRC).