In telecommunication, alongitudinal redundancy check (LRC), orhorizontal redundancy check, is a form ofredundancy check that is applied independently to each of a parallel group of bit streams. The data must be divided intotransmission blocks, to which the additional check data is added.
The term usually applies to a singleparity bit per bit stream, calculated independently of all the other bit streams (BIP-8).[1][2]
This "extra" LRC word at the end of a block of data is very similar tochecksum andcyclic redundancy check (CRC).
While simple longitudinalparity can onlydetect errors, it can be combined with additional error-control coding, such as atransverse redundancy check (TRC), tocorrect errors. The transverse redundancy check is stored on a dedicated "parity track".
Whenever any single-bit error occurs in a transmission block of data, such two-dimensional parity checking, or "two-coordinate parity checking",[3]enables the receiver to use the TRC to detect which byte the error occurred in, and the LRC to detect exactly which track the error occurred in, to discover exactly which bit is in error, and then correct that bit by flipping it.[4][5][6]
International standardISO 1155[7] states that a longitudinal redundancy check for a sequence of bytes may be computed insoftware by the following algorithm:
lrc := 0for each byteb in the bufferdolrc := (lrc +b)and 0xFFlrc := (((lrc XOR 0xFF) + 1)and 0xFF)
which can be expressed as "the 8-bit two's-complement value of the sum of all bytes modulo 28" (x AND 0xFF is equivalent tox MOD 28).
Many protocols use an XOR-based longitudinal redundancy check byte (often calledblock check character or BCC), including the serial line interface protocol (SLIP, not to be confused with the later and well-knownSerial LineInternet Protocol),[8]theIEC 62056-21 standard for electrical-meter reading, smart cards as defined inISO/IEC 7816, and theACCESS.bus protocol.
An 8-bit LRC such as this is equivalent to acyclic redundancy check using the polynomialx8 + 1, but the independence of the bit streams is less clear when looked at in that way.
This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22. (in support ofMIL-STD-188).