# Longitudinal redundancy check

In telecommunication, a longitudinal redundancy check (LRC), or horizontal redundancy check, is a form of redundancy check that is applied independently to each of a parallel group of bit streams. 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 (BIP-8),[1][2] although it could also be used to refer to a larger Hamming code.

This "extra" LRC word at the end of a block of data is very similar to checksum and cyclic redundancy check (CRC).

## Optimal rectangular code

While simple longitudinal parity can only detect errors, it can be combined with additional error-control coding, such as a transverse redundancy check (TRC), to correct 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]

## Pseudocode

International standard ISO 1155[7] states that a longitudinal redundancy check for a sequence of bytes may be computed in software by the following algorithm:

```Set LRC = 0
For each byte b in the buffer
do
Set LRC = (LRC + b) AND 0xFF
end do
Set LRC = (((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 to `x MOD 28`).

Many protocols use an XOR-based longitudinal redundancy check byte (often called block check character or BCC), including the serial line internet protocol (SLIP),[8] the IEC 62056-21 standard for electrical-meter reading, smart cards as defined in ISO/IEC 7816, and the ACCESS.bus protocol.

An 8-bit LRC such as this is equivalent to a cyclic redundancy check using the polynomial x8 + 1, but the independence of the bit streams is less clear when looked at in that way.

## References

1. ^ RFC 935: "Reliable link layer protocols".
2. ^
3. ^ [1].
4. ^ Gary H. Kemmetmueller. "RAM error correction using two dimensional parity checking".
5. ^ Oosterbaan. "Longitudinal parity".
6. ^
7. ^
8. ^ RFC 914. "A Thinwire Protocol for connecting personal computers to the INTERNET". Appendix D: "Serial Line Interface Protocol (SLIP)".
Binary Synchronous Communications

Binary Synchronous Communication (BSC or Bisync) is an IBM character-oriented, half-duplex link protocol, announced in 1967 after the introduction of System/360. It replaced the synchronous transmit-receive (STR) protocol used with second generation computers. The intent was that common link management rules could be used with three different character encodings for messages. Six-bit Transcode looked backwards to older systems; USASCII with 128 characters and EBCDIC with 256 characters looked forward. Transcode disappeared very quickly but the EBCDIC and USASCII dialects of Bisync continued in use.

At one time Bisync was the most widely used communications protocol and is still in limited use in 2013.

Check digit

A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually. It is analogous to a binary parity bit used to check for errors in computer-generated data. It consists of one or more digits computed by an algorithm from the other digits (or letters) in the sequence input.

With a check digit, one can detect simple errors in the input of a series of characters (usually digits) such as a single mistyped digit or some permutations of two successive digits.

Derived unique key per transaction

In cryptography, Derived Unique Key Per Transaction (DUKPT) is a key management scheme in which for every transaction, a unique key is used which is derived from a fixed key. Therefore, if a derived key is compromised, future and past transaction data are still protected since the next or prior keys cannot be determined easily. DUKPT is specified in ANSI X9.24 part 1.

ISO/IEC 7813

ISO/IEC 7813 is an international standard codified by the International Organization for Standardization and International Electrotechnical Commission that defines properties of financial transaction cards, such as ATM or credit cards.

Immunity-aware programming

When writing firmware for an embedded system, immunity-aware programming refers to programming techniques which improve the tolerance of transient errors in the program counter or other modules of a program that would otherwise lead to failure. Transient errors are typically caused by single event upsets, insufficient power, or by strong electromagnetic signals transmitted by some other "source" device.

Immunity-aware programming is an example of defensive programming and EMC-aware programming. Although most of these techniques apply to the software in the "victim" device to make it more reliable, a few of these techniques apply to software in the "source" device to make it emit less unwanted noise.

Index of electronics articles

This is an index of articles relating to electronics and electricity or natural electricity and things that run on electricity and things that use or conduct electricity.

List of algorithms

The following is a list of algorithms along with one-line descriptions for each.

Longitudinal

Longitudinal is a geometric term of location which may refer to:

Longitude

Line of longitude, also called a meridian

Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicle, front to back

Longitudinal mode, a particular standing wave pattern of a resonant cavity formed by waves confined in the cavity

Longitudinal redundancy check, in telecommunication, a form of redundancy check that is applied independently to each of a parallel group of bit streams.

Longitudinal study, a research study that involves repeated observations of the same items over long periods of time — often many decades

Longitudinal voltage, in telecommunication, a voltage induced or appearing along the length of a transmission medium

Longitudinal wave, a wave with oscillations or vibrations along or parallel to their direction of travel

Longitudinal/longitudinally are also anatomical terms of location.

Magnetic stripe card

A magnetic stripe card is a type of card capable of storing data by modifying the magnetism of tiny iron-based magnetic particles on a band of magnetic material on the card. The magnetic stripe, sometimes called swipe card or magstripe, is read by swiping past a magnetic reading head. Magnetic stripe cards are commonly used in credit cards, identity cards, and transportation tickets. They may also contain an RFID tag, a transponder device and/or a microchip mostly used for business premises access control or electronic payment.

Magnetic recording on steel tape and wire was invented in Denmark around 1900 for recording audio. In the 1950s, magnetic recording of digital computer data on plastic tape coated with iron oxide was invented. In 1960, IBM used the magnetic tape idea to develop a reliable way of securing magnetic stripes to plastic cards, under a contract with the US government for a security system. A number of International Organization for Standardization standards, ISO/IEC 7810, ISO/IEC 7811, ISO/IEC 7812, ISO/IEC 7813, ISO 8583, and ISO/IEC 4909, now define the physical properties of the card, including size, flexibility, location of the magstripe, magnetic characteristics, and data formats. They also provide the standards for financial cards, including the allocation of card number ranges to different card issuing institutions.

Modbus

Modbus is a serial communications protocol originally published by Modicon (now Schneider Electric) in 1979 for use with its programmable logic controllers (PLCs). Modbus has become a de facto standard communication protocol and is now a commonly available means of connecting industrial electronic devices. The main reasons for the use of Modbus in the industrial environment are:

developed with industrial applications in mind,

openly published and royalty-free,

easy to deploy and maintain,

moves raw bits or words without placing many restrictions on vendors.Modbus enables communication among many devices connected to the same network, for example, a system that measures temperature and humidity and communicates the results to a computer. Modbus is often used to connect a supervisory computer with a remote terminal unit (RTU) in supervisory control and data acquisition (SCADA) systems. Many of the data types are named from industry usage of Ladder logic and its use in driving relays: a single-bit physical output is called a coil, and a single-bit physical input is called a discrete input or a contact.

The development and update of Modbus protocols has been managed by the Modbus Organization since April 2004, when Schneider Electric transferred rights to that organization. The Modbus Organization is an association of users and suppliers of Modbus-compliant devices that advocates for the continued use of the technology.

Parity bit

A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd. Parity bits are used as the simplest form of error detecting code.

There are two variants of parity bits: even parity bit and odd parity bit.

In the case of even parity, for a given set of bits, the occurrences of bits whose value is 1 is counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0.

In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number. If the count of bits with a value of 1 is odd, the count is already odd so the parity bit's value is 0.

Even parity is a special case of a cyclic redundancy check (CRC), where the 1-bit CRC is generated by the polynomial x+1.

If a bit is present at a point otherwise dedicated to a parity bit, but is not used for parity, it may be referred to as a mark parity bit if the parity bit is always 1, or a space parity bit if the bit is always 0. In such cases where the value of the bit is constant, it may be called a stick parity bit even though its function has nothing to do with parity. The function of such bits varies with the system design, but examples of functions for such bits include timing management, or identification of a packet as being of data or address significance. If its actual bit value is irrelevant to its function, the bit amounts to a don't-care term.Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), although they can also be applied separately to an entire message string of bits.

Synchronous transmit-receive (STR) was an early IBM character-oriented communications protocol which preceded Bisync. STR was point-to-point only, and employed a four-of-eight transmission code, communicating at up to 5100 characters per second over half-duplex or full-duplex communication lines.

The IBM 1009 Data Transmission Unit, the IBM 1130 Synchronous Communications Adapter, the IBM System/360 model 20 Communications Adapter, and the IBM 2701 Data Transmission Unit provided host computer support for STR.

The IBM 7701, the IBM 7702 Magnetic Tape Transmission Terminal, the IBM 1013 Card Transmission Terminal, and the IBM 7710 and IBM 7711 Data Communication Units were among the remote devices supported by STR.STR was still supported as of 1972, although it had generally faded from use.

Transverse redundancy check

In telecommunications, a transverse redundancy check (TRC) or vertical redundancy check is a redundancy check for synchronized parallel bits applied once per bit time, across the bit streams. This requires additional parallel channels for the check bit or bits.

The term usually applies to a single parity bit, although it could also be used to refer to a larger Hamming code.

The adjective "transverse" is most often used when it is used in combination with additional error control coding, such as a longitudinal redundancy check. Although parity alone can only detect and not correct errors, it can be part of a system for correcting errors.

An example of a TRC is the parity written to the 9th track of a 9 track tape.

ISO standards by standard number
1–9999
10000–19999
20000+

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