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Long-haul communications

In telecommunication, the term long-haul communications has the following meanings:

1. In public switched networks, pertaining to circuits that span large distances, such as the circuits in inter-LATA, interstate, and international communications. See also Long line (telecommunications)

2. In the military community, communications among users on a national or worldwide basis.

Note 1: Compared to tactical communications, long-haul communications are characterized by (a) higher levels of users, such as the US National Command Authority, (b) more stringent performance requirements, such as higher quality circuits, (c) longer distances between users, including worldwide distances, (d) higher traffic volumes and densities, (e) larger switches and trunk cross sections, and (f) fixed and recoverable assets.

Note 2: "Long-haul communications" usually pertains to the U.S. Defense Communications System.

 Note 3: "Long-haul telecommunications technicians" can be translated into many fields of IT work within the corporate industry (Information Technology, Network Technician, Telecommunication Specialist, It Support, and so on). While the term is used in military most career fields that are in communications such as 3D1X2 - Cyber Transport Systems (the career field has been renamed so many times over the course of many years but essentially it is the same job (Network Infrastructure Tech., Systems Control Technician, and Cyber Transport Systems)) or may work in areas that require the "in between" (cloud networking) for networks (MSPP, ATM, Routers, Switches), phones (VOIP, DS0 - DS4 or higher, and so on), encryption (configuring encryption devices or monitoring), and video support data transfers. The "bulk data transfer" or aggregation networking.

The Long-haul telecommunication technicians is considered a "jack of all" but it is much in the technician's interest to gather greater education with certifications to qualify for certain jobs outside the military. The Military provides an avenue but does not make the individual a master of the career field. The technician will find that the job out look outside of military requires many things that aren't required of them within the career field while in the military. So it is best to find the job that is similar to the AFSC and also view the companies description of the qualification to fit that job. Also at least get an associate degree, over 5 years experience, and all of the required "certs" (Network +, Security +, CCNA, CCNP and so on) to acquire the job or at least an interview. The best time to apply or get a guaranteed job is the last three months before you leave the military. Military personnel that are within the career field 3D1X2 require a Secret, TS, or TS with SCI clearance in order to do the job.

title: Long-haul communications


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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).

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", 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.

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

lrc := 0 for each byte b in the buffer do lrc := (lrc + b) and 0xFF 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" ( is equivalent to  ).

Other forms
Many protocols use an XOR-based longitudinal redundancy check byte (often called block check character or BCC), including the serial line interface protocol (SLIP, not to be confused with the later and well-known Serial Line Internet Protocol), 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.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Longitudinal redundancy check


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Long-term stability

In electronics, the long-term stability of an oscillator is the degree of uniformity of frequency over time, when the frequency is measured under identical environmental conditions, such as supply voltage, load, and temperature. Long-term frequency changes are caused by changes in the oscillator elements that determine frequency, such as crystal drift, inductance changes, and capacitance changes.

title: Long-term stability


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Loop gain

In electronics and control system theory, loop gain is the sum of the gain, expressed as a ratio or in decibels, around a feedback loop. Feedback loops are widely used in electronics in amplifiers and oscillators, and more generally in both electronic and nonelectronic industrial control systems to control industrial plant and equipment. The concept is also used in biology. In a feedback loop, the output of a device, process or plant is sampled and applied to alter the input, to better control the output. The loop gain, along with the related concept of loop phase shift, determines the behavior of the device, and particularly whether the output is stable, or unstable, which can result in oscillation. The importance of loop gain as a parameter for characterizing electronic feedback amplifiers was first recognized by Heinrich Barkhausen in 1921, and was developed further by Hendrik Wade Bode and Harry Nyquist at Bell Labs in the 1930s.

A block diagram of an electronic amplifier with negative feedback is shown at right. The input signal is applied to the amplifier with open-loop gain A and amplified. The output of the amplifier is applied to a feedback network with gain β, and subtracted from the input to the amplifier. The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied. In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, −Aβ. The minus sign is because the feedback signal is subtracted from the input.

The gains A and β, and therefore the loop gain, generally vary with the frequency of the input signal, and so are usually expressed as functions of the angular frequency ω in radians per second. It is often displayed as a graph with the horizontal axis frequency ω and the vertical axis gain. In amplifiers, the loop gain is the difference between the open-loop gain curve and the closed-loop gain curve (actually, the 1/β curve) on a dB scale.

title: Loop gain


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LPD433

LPD433 (low power device 433 MHz) is a UHF band in which license free communication devices are allowed to operate in some regions. The frequencies correspond with the ITU region 1 ISM band of 433.050 MHz to 434.790 MHz. The frequencies used are within the 70-centimeter band, which is currently otherwise reserved for government and amateur radio operations in the United States and most nations worldwide.

LPD hand-held radios are authorized for licence-free voice communications use in most of Europe using analog frequency modulation (FM) as part of short range device regulations, with 25 kHz channel spacing, for a total of 69 channels. In some countries, LPD devices may only be used with an integral and non-removable antenna with a maximum legal power output of 10 mW.

Voice communication in the LPD band was introduced to reduce the burden on the eight (now sixteen) PMR446 channels over shorter ranges (less than 1 km).

LPD is also used in vehicle key-less entry device, garage or gate openers and some outdoor home weather station products.

Usage by country
ITU Region 1 (Europe)

United Kingdom

In the UK, LPD433 equipment that meets the respective Ofcom Interface Requirement can be used for model control, analogue/digitised voice and remote keyless entry systems. There is significant scope for interference however, both on frequency and on adjacent frequencies, as the band is far from free. The frequencies from 430 to 440 MHz are allocated on a secondary basis to licensed radio amateurs who are allowed to use up to 40 W (16 dBW) between 430 and 432 MHz and 400 W (26 dBW) between 432 and 440 MHz. Channels 1 to 14 are UK amateur repeater outputs and channels 62 to 69 are UK amateur repeater inputs. This band is shared on a secondary basis for both licensed and licence exempt users, with the primary user being the Ministry of Defence.

Ofcom, together with the RSGB Emerging Technology Co-ordination Committee have produced guidelines to help mitigate the side effects of interference to an extent.

Switzerland

Switzerland permits the use of all 69 LPD433 channels with a maximum power output of 10 mW.

Spain

According to a recently published (June 2021) resolution of the Spanish government, where it defines 'interface IR-266', non-specific mobile short-range devices may be used without authorization for voice applications with 'advanced mitigation techniques' (such as listening before talking ) from 434.040 to 434.790 MHz, with channels narrower than 25 kHz and with a maximum 'apparent radiated power' of 10 mW. This would make the use of LPD433 channels 40 to 69 possible in Spain.

Other European countries

European remote keyless entry systems often use the 433 MHz band, although, as in all of Europe, these frequencies are within the 70-centimeter band allocated to amateur radio, and interference results. In Germany, before the end of 2008, radio control enthusiasts were able to use frequencies from channel 03 through 67 for radio control of any form of model (air or ground-based), all with odd channel numbers (03, 05, etc. up to ch. 67), with each sanctioned frequency having 50 kHz of bandwidth separation between each adjacent channel.

ITU Region 2 (America)

In ITU region 2 (the Americas), the frequencies that LPD433 uses are also within the 70-centimeter band allocated to amateur radio. In the United States LPD433 radios can only be used under FCC amateur regulations by properly licensed amateur radio operators.

ITU Region 3

Malaysia

In Malaysia, this band is also within the 70-centimeter band (430.000 – 440.000 MHz) allocated to amateur radio. Class B amateur radio holders are permitted to transmit up to 50 watts PEP power level. There is no licence requirement for LPD as long as it complies with requirement regulated by Malaysian Communications And Multimedia Commission (MCMC). As regulated by MCMC in Technical Code for Short Range Devices, remote control and security device are allowed up to 50 mW ERP and up to 100 mW ERP for Short Range Communication (SRC) devices. RFID are allowed up to 100 mW EIRP.

title: LPD433


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Machine-readable medium and data

In communications and computing, a machine-readable medium (or computer-readable medium) is a medium capable of storing data in a format easily readable by a digital computer or a sensor. It contrasts with human-readable medium and data.

The result is called machine-readable data or computer-readable data, and the data itself can be described as having machine-readability.

Data
Machine-readable data must be structured data.

Attempts to create machine-readable data occurred as early as the 1960s. At the same time that seminal developments in machine-reading and natural-language processing were releasing (like Weizenbaum's ELIZA), people were anticipating the success of machine-readable functionality and attempting to create machine-readable documents. One such example was musicologist Nancy B. Reich's creation of a machine-readable catalog of composer William Jay Sydeman's works in 1966.

In the United States, the OPEN Government Data Act of 14 January 2019 defines machine-readable data as "data in a format that can be easily processed by a computer without human intervention while ensuring no semantic meaning is lost." The law directs U.S. federal agencies to publish public data in such a manner, ensuring that "any public data asset of the agency is machine-readable".

Machine-readable data may be classified into two groups: human-readable data that is marked up so that it can also be read by machines (e.g. microformats, RDFa, HTML), and data file formats intended principally for processing by machines (CSV, RDF, XML, JSON). These formats are only machine readable if the data contained within them is formally structured; exporting a CSV file from a badly structured spreadsheet does not meet the definition.

Machine readable is not synonymous with digitally accessible. A digitally accessible document may be online, making it easier for humans to access via computers, but its content is much harder to extract, transform, and process via computer programming logic if it is not machine-readable.

Extensible Markup Language (XML) is designed to be both human- and machine-readable, and Extensible Stylesheet Language Transformation (XSLT) is used to improve the presentation of the data for human readability. For example, XSLT can be used to automatically render XML in Portable Document Format (PDF). Machine-readable data can be automatically transformed for human-readability but, generally speaking, the reverse is not true.

For purposes of implementation of the Government Performance and Results Act (GPRA) Modernization Act, the Office of Management and Budget (OMB) defines "machine readable format" as follows: "Format in a standard computer language (not English text) that can be read automatically by a web browser or computer system. (e.g.; xml). Traditional word processing documents and portable document format (PDF) files are easily read by humans but typically are difficult for machines to interpret. Other formats such as extensible markup language (XML), (JSON), or spreadsheets with header columns that can be exported as comma separated values (CSV) are machine readable formats. As HTML is a structural markup language, discreetly labeling parts of the document, computers are able to gather document components to assemble tables of contents, outlines, literature search bibliographies, etc. It is possible to make traditional word processing documents and other formats machine readable but the documents must include enhanced structural elements."

Media
Examples of machine-readable media include magnetic media such as magnetic disks, cards, tapes, and drums, punched cards and paper tapes, optical discs, barcodes and magnetic ink characters.

Common machine-readable technologies include magnetic recording, processing waveforms, and barcodes. Optical character recognition (OCR) can be used to enable machines to read information available to humans. Any information retrievable by any form of energy can be machine-readable.

Examples include:

 * Acoustics
 * Chemical
 * Photochemical
 * Electrical
 * Semiconductor used in volatile RAM microchips
 * Floating-gate transistor used in non-volatile memory cards
 * Radio transmission
 * Magnetic storage
 * Mechanical
 * Tins And Swins
 * Punched card
 * Paper tape
 * Music roll
 * Music box cylinder or disk
 * Grooves (See also: Audio Data)
 * Phonograph cylinder
 * Gramophone record
 * DictaBelt (groove on plastic belt)
 * Capacitance Electronic Disc
 * Optics
 * Optical storage
 * Thermodynamic

title: Machine-readable medium and data


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Magneto-ionic double refraction

In telecommunication, magneto-ionic double refraction is the combined effect of the Earth's magnetic field and atmospheric ionization, whereby a linearly polarized wave entering the ionosphere is split into two components called the ordinary wave and extraordinary wave.

The component waves follow different paths, experience different attenuations, have different phase velocities, and, in general, are elliptically polarized in opposite senses. The critical frequency of the extraordinary wave is always greater than the critical frequency of the ordinary wave (i.e. the wave in absence of the magnetic field) by the amount approximately equal to .5 times of gyro frequency. The amplitude of extraordinary wave is dependent on the earth magnetic field at that particular point. Beside splitting, the polarization of the incident radio wave is also effected by this phenomenon because the electron that were earlier in simple harmonic motion only are now in spiral motion too due to the magnetic field.

title: Magneto-ionic double refraction


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Magneto-optic effect

A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a medium, which is also called gyrotropic or gyromagnetic, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect).

In general, magneto-optic effects break time reversal symmetry locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical isolators (through which light passes in one direction but not the other).

Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers.

Gyrotropic permittivity
In particular, in a magneto-optic material the presence of a magnetic field (either externally applied or because the material itself is ferromagnetic) can cause a change in the permittivity tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with complex off-diagonal components, depending on the frequency ω of incident light. If the absorption losses can be neglected, ε is a Hermitian matrix. The resulting principal axes become complex as well, corresponding to elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to birefringence).

More specifically, for the case where absorption losses can be neglected, the most general form of Hermitian ε is:

 * $$\varepsilon = \begin{pmatrix}

\varepsilon_{xx}' & \varepsilon_{xy}' + i g_z & \varepsilon_{xz}' - i g_y \\ \varepsilon_{xy}' - i g_z & \varepsilon_{yy}' & \varepsilon_{yz}' + i g_x \\ \varepsilon_{xz}' + i g_y & \varepsilon_{yz}' - i g_x & \varepsilon_{zz}' \\ \end{pmatrix}$$

or equivalently the relationship between the displacement field D and the electric field E is:

 * $$\mathbf{D} = \varepsilon \mathbf{E} = \varepsilon' \mathbf{E} + i \mathbf{E} \times \mathbf{g}$$

where $$\varepsilon'$$ is a real symmetric matrix and $$\mathbf{g} = (g_x,g_y,g_z)$$ is a real pseudovector called the gyration vector, whose magnitude is generally small compared to the eigenvalues of $$\varepsilon'$$. The direction of g is called the axis of gyration of the material. To first order, g is proportional to the applied magnetic field:

 * $$\mathbf{g} = \varepsilon_0 \chi^{(m)} \mathbf{H}$$

where $$\chi^{(m)} \!$$ is the magneto-optical susceptibility (a scalar in isotropic media, but more generally a tensor). If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation (somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field).

The simplest case to analyze is the one in which g is a principal axis (eigenvector) of $$\varepsilon'$$, and the other two eigenvalues of $$\varepsilon'$$ are identical. Then, if we let g lie in the z direction for simplicity, the ε tensor simplifies to the form:

 * $$\varepsilon = \begin{pmatrix}

\varepsilon_1 & + i g_z & 0 \\ - i g_z & \varepsilon_1 & 0 \\ 0 & 0 & \varepsilon_2 \\ \end{pmatrix}$$

Most commonly, one considers light propagating in the z direction (parallel to g). In this case the solutions are elliptically polarized electromagnetic waves with phase velocities $$1 / \sqrt{\mu(\varepsilon_1 \pm g_z)}$$ (where μ is the magnetic permeability). This difference in phase velocities leads to the Faraday effect.

For light propagating purely perpendicular to the axis of gyration, the properties are known as the Cotton-Mouton effect and used for a Circulator.

Kerr rotation and Kerr ellipticity
Kerr rotation and Kerr ellipticity are changes in the polarization of incident light which comes in contact with a gyromagnetic material. Kerr rotation is a rotation in the plane of polarization of transmitted light, and Kerr ellipticity is the ratio of the major to minor axis of the ellipse traced out by elliptically polarized light on the plane through which it propagates. Changes in the orientation of polarized incident light can be quantified using these two properties.

According to classical physics, the speed of light varies with the permittivity of a material:

$$v_p = \frac{1}{\sqrt{\epsilon \mu}} $$

where $$v_p$$ is the velocity of light through the material, $$\epsilon$$ is the material permittivity, and $$\mu$$ is the material permeability. Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.

This can be better understood if we consider a wave of light that is circularly polarized (seen to the right). If this wave interacts with a material at which the horizontal component (green sinusoid) travels at a different speed than the vertical component (blue sinusoid), the two components will fall out of the 90 degree phase difference (required for circular polarization) changing the Kerr ellipticity.

A change in Kerr rotation is most easily recognized in linearly polarized light, which can be separated into two circularly polarized components: Left-handed circular polarized (LHCP) light and right-handed circular polarized (RHCP) light. The anisotropy of the magneto-optic material permittivity causes a difference in the speed of LHCP and RHCP light, which will cause a change in the angle of polarized light. Materials that exhibit this property are known as birefringent.

From this rotation, we can calculate the difference in orthogonal velocity components, find the anisotropic permittivity, find the gyration vector, and calculate the applied magnetic field $$\mathbf{H}$$.

title: Magneto-optic effect


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Main distribution frame

In telephony, a main distribution frame (MDF or main frame) is a signal distribution frame for connecting equipment (inside plant) to cables and subscriber carrier equipment (outside plant).

Overview
The MDF is a termination point within the local telephone exchange where exchange equipment and terminations of local loops are connected by jumper wires at the MDF. All cable copper pairs supplying services through user telephone lines are terminated at the MDF and distributed through the MDF to equipment within the local exchange e.g. repeaters and DSLAM. Cables to intermediate distribution frames (IDF) terminate at the MDF. Trunk cables may terminate on the same MDF or on a separate trunk main distribution frame (TMDF).

Like other distribution frames the MDF provides flexibility in assigning facilities, at lower cost and higher capacity than a patch panel.

The most common kind of large MDF is a long steel rack accessible from both sides. On one side, termination blocks are arranged horizontally at the front of rack shelves. Jumpers lie on the shelves and go through an insulated steel hoop to run vertically to other termination blocks that are arranged vertically. There is a hoop or ring at the intersection of each level and each vertical. Installing a jumper historically required two workers, one on either side of the MDF. The shelves are shallow enough to allow the rings to be within arm's reach, but the workers prefer to hang the jumper on a hook on a pole so their partner can pull it through the ring. A fanning strip at the back of each termination block prevents the wires from covering each other's terminals. With disciplined administration, the MDF can hold over a hundred thousand jumpers, with dozens changed every day, for decades without tangling.

The MDF usually holds telephone exchange protective devices including heat coils, and functions as a test point between a line and the exchange equipment.

History
Before 1960, MDF jumpers were generally soldered. This was reliable but slow and expensive. Wire wrap was introduced in the 1960s, and punch blocks in the 1970s. In most exchanges in the UK, soldered blocks are still in use, but are being slowly phased out.

Each jumper is a twisted pair. Middle 20th century jumper wires in the USA were 24 AWG single strand copper, with a soft polyethylene inner jacket and a cotton wrapper, impregnated to make it slightly brittle and easy to remove neatly. Late 20th century ones had a single, thicker coating of polyethylene cross-linked to provide a suitable degree of brittleness.

Some urban telephone exchange MDFs are two stories high so they do not have to be more than a city block long. A few are three stories. Access to the upper levels can be either by a traveling ladder attached to the MDF, or by mezzanine walkways at a suitable height. By British custom the cables to the outside world are terminated on the horizontal side, and the indoors equipment on the vertical side. American usage is the opposite. Smaller MDFs, and some modern large ones, are single sided so one worker can install, remove or change a jumper. COSMOS and other computerized Operations Support Systems help by assigning terminals close to one another, so most jumpers need not be long and shelves on either type of MDF do not become congested. This database keeps track of all terminals and jumpers. In the early and middle 20th century these records were kept as pencil entries in ledger books. The later database method saves much labor by permitting old jumpers to be reused for new lines.

The adoption of distributed switching in the late 20th century diminished the need for large, active, central MDFs.

Sometimes the MDF is combined with other kinds of distribution frame in a CDF.

The MDF in a private branch exchange performs functions similar to those performed by the MDF in a central office.

Automated Main Distribution Frame (AMDF) has been a subject of experiments.

title: Main distribution frame


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Main lobe

In a radio antennas, the main lobe or main beam is the region of the radiation pattern containing the highest power or exhibiting the greatest field strength.

The radiation pattern of most antennas shows a pattern of "lobes" at various directions, where the radiated signal strength reaches a local maximum, separated by "nulls", at which the radiation falls to zero. In a directional antenna in which the objective is to emit the radio waves in one direction, the lobe in that direction is designed to have higher field strength than the others, so on a graph of the radiation pattern it appears biggest; this is the main lobe. The other lobes are called "sidelobes", and usually represent unwanted radiation in undesired directions. The sidelobe in the opposite direction from the main lobe is called the "backlobe".

The radiation pattern referred to above is usually the horizontal radiation pattern, which is plotted as a function of azimuth about the antenna, although the vertical radiation pattern may also have a main lobe. The beamwidth of the antenna is the width of the main lobe, usually specified by the half power beam width (HPBW), the angle encompassed between the points on the side of the lobe where the power has fallen to half (-3 dB) of its maximum value.

The concepts of main lobe and sidelobes also apply to acoustics and optics, and are used to describe the radiation pattern of optical systems like telescopes, and acoustic transducers like microphones and loudspeakers.

title: Main lobe


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Maintainability

Maintainability is the ease of maintaining or providing maintenance for a functioning product or service. Depending on the field, it can have slightly different meanings.

Engineering
In engineering, maintainability is the ease with which a product can be maintained to:
 * correct defects or their cause,
 * Repair or replace faulty or worn-out components without having to replace still working parts,
 * prevent unexpected working conditions,
 * maximize a product's useful life,
 * maximize efficiency, reliability, and safety,
 * meet new requirements,
 * make future maintenance easier, or
 * cope with a changing environment.

In some cases, maintainability involves a system of continuous improvement - learning from the past to improve the ability to maintain systems, or improve the reliability of systems based on maintenance experience.

Telecommunication
In telecommunication and several other engineering fields, the term maintainability has the following meanings:

 * A characteristic of design and installation, expressed as the probability that an item will be retained in or restored to a specified condition within a given period of time, when the maintenance is performed by prescribed procedures and resources.
 * The ease with which maintenance of a functional unit can be performed by prescribed requirements.

Software
In software engineering, these activities are known as software maintenance (cf. ISO/IEC 9126). Closely related concepts in the software engineering domain are evolvability, modifiability, technical debt, and code smells.

The maintainability index is calculated with certain formulae from lines-of-code measures, McCabe measures and Halstead complexity measures.

The measurement and tracking of maintainability are intended to help reduce or reverse a system's tendency toward "code entropy" or degraded integrity, and to indicate when it becomes cheaper and/or less risky to rewrite the code than it is to change it.

title: Maintainability


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Maintenance (disambiguation)

Maintenance may refer to:

Biological science

 * Maintenance of an organism
 * Maintenance respiration

Non-technical maintenance

 * Alimony, also called maintenance in British English
 * Champerty and maintenance, two related legal doctrines
 * Child support, also commonly called "child maintenance"
 * Feudal maintenance, system of funding armies

Technical maintenance

 * Maintenance (technical)
 * Aircraft maintenance
 * Bicycle maintenance
 * Bus maintenance
 * Car maintenance
 * Train maintenance
 * Property maintenance
 * Railroad track maintenance
 * Software maintenance

Some kinds of technical maintenance

 * Condition-based maintenance
 * Corrective maintenance
 * Planned maintenance
 * Predictive maintenance
 * Preventive maintenance
 * Total productive maintenance

title: Maintenance (disambiguation)


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Managed object

In telecommunication, the term managed object has the following meanings:

1. In a network, an abstract representation of network resources that are managed. With "representation", we mean not only the actual device that is managed, but also the device driver, that communicates with the device. An example of a printer as a managed object is the window that shows information about the printer, such as the location, printer status, printing progress, paper choice, and printing margins.

The database, where all managed objects are stored, is called Management Information Base. In contrast with a CI, a managed object is "dynamic" and communicates with other network resources that are managed.

Note: A managed object may represent a physical entity, a network service, or an abstraction of a resource that exists independently of its use in management.

2. In telecommunications management, a resource within the telecommunications environment that may be managed through the use of operation, administration, maintenance, and provisioning (OAMP) application protocols.

title: Managed object


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Manchester code

In telecommunication and data storage, Manchester code (also known as phase encoding, or PE) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time. It is a self-clocking signal with no DC component. Consequently, electrical connections using a Manchester code are easily galvanically isolated.

Manchester code derives its name from its development at the University of Manchester, where the coding was used for storing data on the magnetic drums of the Manchester Mark 1 computer.

Manchester code was widely used for magnetic recording on 1600 bpi computer tapes before the introduction of 6250 bpi tapes which used the more efficient group-coded recording. Manchester code was used in early Ethernet physical layer standards and is still used in consumer IR protocols, RFID and near-field communication.

Features
Manchester coding is a special case of binary phase-shift keying (BPSK), where the data controls the phase of a square wave carrier whose frequency is the data rate. Manchester code ensures frequent line voltage transitions, directly proportional to the clock rate; this helps clock recovery.

The DC component of the encoded signal is not dependent on the data and therefore carries no information. Therefore connections may be inductively or capacitively coupled, allowing the signal to be conveyed conveniently by galvanically isolated media (e.g., Ethernet) using a network isolator—a simple one-to-one pulse transformer which cannot convey a DC component.

Limitations
Manchester coding's data rate is only half that of a non-coded signal, which limits its usefulness to systems where bandwidth is not an issue, such as a local area network (LAN).

Manchester encoding introduces difficult frequency-related problems that make it unsuitable for use at higher data rates.

There are more complex codes, such as 8B/10B encoding, that use less bandwidth to achieve the same data rate but may be less tolerant of frequency errors and jitter in the transmitter and receiver reference clocks.

Encoding and decoding

Manchester code always has a transition at the middle of each bit period and may (depending on the information to be transmitted) have a transition at the start of the period also. The direction of the mid-bit transition indicates the data. Transitions at the period boundaries do not carry information. They exist only to place the signal in the correct state to allow the mid-bit transition.

Conventions for representation of data
There are two opposing conventions for the representations of data.

The first of these was first published by G. E. Thomas in 1949 and is followed by numerous authors (e.g., Andy Tanenbaum). It specifies that for a 0 bit the signal levels will be low–high (assuming an amplitude physical encoding of the data) – with a low level in the first half of the bit period, and a high level in the second half. For a 1 bit the signal levels will be high–low. This is also known as Manchester II or Biphase-L code.

The second convention is also followed by numerous authors (e.g., William Stallings) as well as by IEEE 802.4 (token bus) and lower speed versions of IEEE 802.3 (Ethernet) standards. It states that a logic 0 is represented by a high–low signal sequence and a logic 1 is represented by a low–high signal sequence.

If a Manchester encoded signal is inverted in communication, it is transformed from one convention to the other. This ambiguity can be overcome by using differential Manchester encoding.

Decoding
The existence of guaranteed transitions allows the signal to be self-clocking, and also allows the receiver to align correctly; the receiver can identify if it is misaligned by half a bit period, as there will no longer always be a transition during each bit period. The price of these benefits is a doubling of the bandwidth requirement compared to simpler NRZ coding schemes.

Encoding
Encoding conventions are as follows:
 * Each bit is transmitted in a fixed time (the "period").
 * A  is expressed by a low-to-high transition, a   by high-to-low transition (according to G. E. Thomas's convention – in the IEEE 802.3 convention, the reverse is true).
 * The transitions which signify  or   occur at the midpoint of a period.
 * Transitions at the start of a period are overhead and don't signify data.

title: Manchester code


text:
Mandrel wrapping

In multimode fiber optics, mandrel wrapping is a technique used to preferentially attenuate high-order mode power  of a propagating optical signal. Consequently, if the fibre is propagating substantial energy in affected modes, the modal distribution will be changed.

A cylindrical rod wrap consists of a specified number turns of fiber on a mandrel of specified size, depending on the fibre characteristics and the desired modal distribution. It has application in optical transmission performance tests, to create a defined mode power distribution or to prevent multimode propagation in single mode fibre. If the launch fibre is fully filled ahead of the mandrel wrap, the higher-order modes will be stripped off, leaving only lower-order modes. If the launch fibre is underfilled, for example as a consequence of being energized by a laser diode or edge-emitting LED, there will be no effect on the mode power distribution or loss measurements.

In multimode fibre, mandrel wrapping is used to eliminate the effect of "transient loss", the tendency of high order modes to experience higher loss than lower order modes. Numerical addition (in decibels) of the measured loss of multiple fibre segments and/or components overestimates the loss of the concatenated set if each segment or component has been measured with a full mode power distribution.

In single mode optical fibre measurements, it is used to enforce true single mode propagation at wavelengths near or below the theoretical cutoff wavelength, at which substantial power can exist in a higher order mode group. In this use, it is commonly termed a High Order Mode Filter (HOMF).

Ultimately, the effect of mandrel wrapping on optical measurements depends on the propagating mode power distribution. An additional loss mechanism has no effect unless power is present in the affected modes.

Principle of operation
The effect of physically bending an optical fibre around a cylindrical form is to slightly modify the effective refractive index in the curved region, which locally reduces the effective mode volume of the fibre. This causes optical power in the highest order modes to become unguided, or so weakly guided as to be released into an unbound state, absorbed by the fiber coating or completely ejected from the fibre. The practical effect of mandrel wrapping is to attenuate optical power propagating in the highest order modes. Lower order modes are unaffected, experiencing neither increased loss nor conversion into other modes (mode mixing).

Determination of appropriate mandrel wrap conditions
The mandrel diameter and number of turns are chosen to eliminate certain modes in a reproducible way. It is empirically observed that more than 5 full 360 degree wraps creates little additional loss, so 3 to 5 turns are commonly specified. The mandrel diameter affects how far into the mode volume the modal unbinding occurs. Experimentally, one plots the transmitted power from a wrapped fibre into which a uniform modal power distribution has been excited, as a function of mandrel diameter, maintaining a constant number of turns. This reveals step-like reductions in transmitted power as the diameter decreases, where each step is the point at which the mandrel is beginning to affect the next-lower mode group. For best measurement reproducibility, one would select a diameter that is not near such a transition, although this may not be possible if measurements must be performed over a range of wavelengths. Total mode volume in a fiber is a function of wavelength, so the mandrel diameter at which the mode group transitions occur will change with wavelength.

title: Mandrel wrapping


text:
Margin

Margin may refer to:

Physical or graphical edges

 * Margin (typography), the white space that surrounds the content of a page
 * Continental margin, the zone of the ocean floor that separates the thin oceanic crust from thick continental crust
 * Leaf margin, the edge of a leaf
 * Resection margin, the tissue near a tumor that is removed to ensure that no cancer cells are left behind

Economics and finance

 * Margin of profit, the fraction of revenue that is left after paying expenses
 * Margin (economics), a set of constraints conceptualised as a border
 * Margin (finance), a type of financial collateral used to cover credit risk
 * Contribution margin
 * Gross margin

Figurative edges

 * Margin (machine learning), the distance between a decision boundary and a data point
 * Marginal frequency distribution, in statistics (Frequency distribution § Joint frequency distributions)

Other uses

 * Margins (film), a 2022 Italian film by Niccolò Falsetti
 * The Margin (album), a 1985 album by Peter Hammill
 * The Margin (film), a 1976 French film by Walerian Borowczyk
 * The Margin (novel), a 1967 novel by André Pieyre de Mandiargues; basis for the film
 * Margasin, or Margin, a village in Qazvin Province, Iran
 * USS Margin, a US Navy patrol boat 1918–1919

title: Margin


text:
Maritime broadcast communications net

In telecommunication, a maritime broadcast communications net is a communications net that is used for international distress calling, including international lifeboat, lifecraft, and survival-craft high frequency (HF); aeronautical emergency very high frequency (VHF); survival ultra high frequency (UHF); international calling and safety very high frequency (VHF); combined scene-of-search-and-rescue; and other similar and related purposes.

Note: Basic international distress calling is performed at either medium frequency (MF) or at high frequency (HF).

title: Maritime broadcast communications net


text:
Master frequency generator

A master frequency generator or master electronic oscillator, in frequency-division multiplexing (FDM), is a piece of equipment used to provide system end-to-end carrier frequency synchronization and frequency accuracy of tones.

The following types of oscillators are used in the Defense Communications System FDM systems:
 * Type 1 - A master carrier oscillator as an integral part of the multiplexer set.
 * Type 2 - A submaster oscillator equipment or slave oscillator equipment as an integral part of the multiplexer set.
 * Type 3 - An external master oscillator equipment that has extremely accurate and stable characteristics.

title: Master frequency generator


text:
Master station

In telecommunication, a master station is a station that controls or coordinates the activities of other stations in the system.

Examples:
 * In a data network, the control station may designate a master station to ensure data transfer to one or more slave stations. Such a master station controls one or more data links of the data communications network at any given instant. The assignment of master status to a given station is temporary and is controlled by the control station according to the procedures set forth in the operational protocol. Master status is normally conferred upon a station so that it may transmit a message, but a station need not have a message to send to be designated the master station.
 * In navigation systems using precise time dissemination, the master station is a station that has the clock that is used to synchronize the clocks of subordinate stations.
 * In basic mode link control, the master station is a data station that has accepted an invitation to ensure a data transfer to one or more slave stations. At a given instant, there can be only one master station on a data link.

Operation modes
In data transmission, a master station can be set to not wait for a reply from a slave station after transmitting each message or transmission block. In this case the station is said to be in "continuous operation".

title: Master station


text:
Maximal-ratio combining

In telecommunications, maximum-ratio combining (MRC) is a method of diversity combining in which: It is also known as ratio-squared combining and predetection combining. Maximum-ratio combining is the optimum combiner for independent additive white Gaussian noise channels.
 * 1) the signals from each channel are added together,
 * 2) the gain of each channel is made proportional to the rms signal level and inversely proportional to the mean square noise level in that channel.
 * 3) different proportionality constants are used for each channel.

MRC can restore a signal to its original shape. The technique was invented by American engineer Leonard R. Kahn in 1954.

MRC has also been found in the field of neuroscience, where it has been shown that neurons in the retina scale their dependence on two sources of input in proportion to the signal-to-noise ratio of the inputs.

Example: Least Squares estimate in the case of Rx diversity
We consider an example of which the receiver is endowed with N antennas. In this case, the received vector $$y$$ is

where $$n$$ is noise vector $$n \sim CN(0, I_{N \times N})$$. Following the ML detection criterion the detection procedure may be written as

where $$\mathcal{M}$$ is the considered constellation of $$s$$ and $$\hat{s}$$ is the least square solution to the above model.

The least square solution in this case is also known as maximum-ratio-combining (MRC). In the case of N antennas the LS can be written as

which means that the signal from each antenna is rotated and weighted according to the phase and strength of the channel, such that the signals from all antennas are combined to yield the maximum ratio between signal and noise terms.

title: Maximal-ratio combining


text:
Maximum usable frequency

In radio transmission, maximum usable frequency (MUF) is the highest radio frequency that can be used for transmission between two points on Earth by reflection from the ionosphere (skywave or skip) at a specified time, independent of transmitter power. This index is especially useful for shortwave transmissions.

In shortwave radio communication, a major mode of long distance propagation is for the radio waves to reflect off the ionized layers of the atmosphere and return diagonally back to Earth. In this way radio waves can travel beyond the horizon, around the curve of the Earth. However the refractive index of the ionosphere decreases with increasing frequency, so there is an upper limit to the frequency which can be used. Above this frequency the radio waves are not reflected by the ionosphere but are transmitted through it into space.

The ionization of the atmosphere varies with time of day and season as well as with solar conditions, so the upper frequency limit for skywave communication varies throughout the day. MUF is a median frequency, defined as the highest frequency at which skywave communication is possible 50% of the days in a month, as opposed to the lowest usable high frequency (LUF) which is the frequency at which communication is possible 90% of the days, and the frequency of optimum transmission (FOT).

Typically the MUF is a predicted number. Given the maximum observed frequency (MOF) for a mode on each day of the month at a given hour, the MUF is the highest frequency for which an ionospheric communications path is predicted on 50% of the days of the month.

On a given day, communications may or may not succeed at the MUF. Commonly, the optimal operating frequency for a given path is estimated at 80 to 90% of the MUF. As a rule of thumb the MUF is approximately 3 times the critical frequency.

$$\text{MUF} = \frac{\text{critical frequency}}{\cos\theta}$$

where the critical frequency is the highest frequency reflected for a signal propagating directly upward and θ is the angle of incidence.

Optimum Working Frequency
Another important parameter used in skywave propagation is the optimum working frequency (OWF), which estimates the maximum frequency that must be used for a given critical frequency and incident angle. It is the frequency chosen to avoid the irregularities of the atmosphere.

$$\mathrm{OWF} = 0.85 \mathrm{MUF} = 0.85 f_\mathrm{c} /(cos\theta)$$

title: Maximum usable frequency


text:
Mean time between outages

In a system the mean time between outages (MTBO) is the mean time between equipment failures that result in loss of system continuity or unacceptable degradation.

The MTBO is calculated by the equation,

$$MTBO = \frac{MTBF}{1-FFAS}$$

where MTBF is the nonredundant mean time between failures and FFAS is the fraction of failures for which the failed equipment is automatically bypassed.

title: Mean time between outages


text:
Mechanically induced modulation

Mechanically induced modulation is an optical signal modulation induced by mechanical means.

An example of deleterious mechanically induced modulation is speckle noise created in a multimode fiber by an imperfect splice or imperfectly mated connectors. Mechanical disturbance of the fiber ahead of the joint will introduce changes in the modal structure, resulting in variations of joint loss. This is a subset of many mechanisms that can lead to modal noise in an optical system.

title: Mechanically induced modulation


text:
Mediation function

In telecommunications network management, a mediation function is a function that routes or acts on information passing between network elements and network operations.

Examples of mediation functions are communications control, protocol conversion, data handling, communications of primitives, processing that includes decision-making, and data storage.

Mediation functions can be shared among network elements, mediation devices, and network operation centers.

title: Mediation function


text:
Message

A message is a discrete unit of communication intended by the source for consumption by some recipient or group of recipients. A message may be delivered by various means, including courier, telegraphy, or an electronic bus. A message can be the content of a broadcast. An interactive exchange of messages forms a conversation. The consumption of the message relies on how the recipient interprets the message, there are times where the recipient contradicts the intention of the message which results in a boomerang effect. Message fatigue is another outcome recipients can obtain if a message is conveyed too much by the source.

One example of a message is a press release, which may vary from a brief report or statement released by a public agency to commercial publicity material. Another example of a message is how they are portrayed to a consumer via an advertisement.

Roles in human communication
In communication between humans, messages can be verbal or nonverbal:
 * A verbal message is an exchange of information using words. Examples include face-to-face communication, telephone calls, voicemails, emails, etc.
 * A nonverbal message is communicated through actions or behaviors rather than words, such as conscious or unconscious body language.

The phrase "send a message" or "sending a message" is also used for actions taken by a party to convey that party's attitude towards a certain thing. For example, a government that executes people who commit acts of treason is sending a message that treason will not be tolerated. Conversely, a party that appears through its actions to endorse something that it opposes can be said to be "sending the wrong message", while one which appears to simultaneously endorse contradictory things can be said to be sending "mixed messages".

In computer science
There are two main senses of the word "message" in computing: messages between the human users of computer systems that are delivered by those computer systems, and messages passed between programs or between components of a single program, for their purposes.

 * Instant messaging and emails are examples of computer software designed for delivering human-readable messages in formatted or unformatted text, from one person to another.
 * Message passing is a form of communication used in concurrent and parallel computing, object-oriented programming, and channel communicates, where communication is made by sending messages to recipients. In a related use of this sense of a message, in object-oriented programming language such as main library ["msg" box]Smalltalk or Java, a message is sent to an object, specifying a request for action.

Safety and privacy concerns
Safety and privacy concerns have been expressed in the computer science industry regarding messages. There have been cases where instant messaging apps were found to present a risk of spyware infection. Text messaging is one of the larger causes of distracted driving, and the act of texting and driving has been made illegal in many states as a result.

title: Message


text:
Message format

In telecommunication, a message Base station is a predetermined or prescribed spatial or time-sequential arrangement of the parts of a message that is recorded in or on a data storage medium.

At one time, messages prepared for electrical transmission were composed on a printed blank form with spaces for each part of the message and for administrative entries.

title: Message format


text:
Micro-mainframe link

In telecommunication, a micro-mainframe link is a physical or logical connection established between a remote microprocessor and mainframe host computer for the express purpose of uploading, downloading, or viewing interactive data and databases on-line in real time.

Note: A micro-mainframe link usually requires terminal emulation software on the microcomputer.

title: Micro-mainframe link


text:
Mixer

Mixer may refer to:

Electronics

 * DJ mixer, a type of audio mixing console used by disc jockeys
 * Electronic mixer, electrical circuit for combining signal voltages
 * Frequency mixer, electrical circuit that creates new frequencies from two signals applied to it
 * Mixing console, an electronic device for combining sounds of different audio signals
 * Mix engineer, person who combines elements of recorded music into a final version
 * Mode scrambler, known as a mode mixer, telecommunications device for inducing mode coupling in an optical fiber
 * Sound card mixer, analog part of a sound card that routes and mixes sound signals
 * Vision mixer, an electronic device for combining video signals

Industrial and lab equipment

 * Concrete mixer, a machine which combines the ingredients of concrete, a.k.a. cement mixer
 * Feed mixer, for mixing feed ingredients
 * High-shear mixer, a device that disperse, or transports one phase or ingredient (liquid, solid, gas) into a main continuous phase (liquid)
 * High viscosity mixer
 * Impinging mixer, part of a reaction injection molding system
 * Industrial mixer, a machine for mixing the materials in industrial scale
 * Static mixer, a device for mixing two fluid materials through a tube containing a series of baffles
 * Submersible mixer, a machine used for mixing liquids and slurries in tanks (e.g. wastewater, liquid manure, etc.)
 * Vortex mixer, a laboratory device

Entertainment

 * Mixer (service), a defunct interactive video game streaming platform by Microsoft
 * Mixer dance, a kind of participation dance that involves changing partners
 * Production sound mixer, the head of a film production sound crew
 * Mixer (album), a 2012 album by Desario
 * "The Mixer", a 1991 song by The Fall from Shift-Work
 * The Mixer, a 1992 TV series, starring Simon Williams

Other

 * Mixer (appliance), kitchen appliance used to combine ingredients
 * Mixer (engine), a device for quieting an airplane engine
 * Drink mixer, non-alcoholic ingredients in mixed drinks and cocktails
 * Mixer, an alternate name for a singles event

title: Mixer


text:
Sprague–Grundy theorem

In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim. It can therefore be represented as a natural number, the size of the heap in its equivalent game of nim, as an ordinal number in the infinite generalization, or alternatively as a nimber, the value of that one-heap game in an algebraic system whose addition operation combines multiple heaps to form a single equivalent heap in nim.

The Grundy value or nim-value of any impartial game is the unique nimber that the game is equivalent to. In the case of a game whose positions are indexed by the natural numbers (like nim itself, which is indexed by its heap sizes), the sequence of nimbers for successive positions of the game is called the nim-sequence of the game.

The Sprague–Grundy theorem and its proof encapsulate the main results of a theory discovered independently by R. P. Sprague (1936) and P. M. Grundy (1939).

Definitions
For the purposes of the Sprague–Grundy theorem, a game is a two-player sequential game of perfect information satisfying the ending condition (all games come to an end: there are no infinite lines of play) and the normal play condition (a player who cannot move loses).

At any given point in the game, a player's position is the set of moves they are allowed to make. As an example, we can define the zero game to be the two-player game where neither player has any legal moves. Referring to the two players as $$A$$ (for Alice) and $$B$$ (for Bob), we would denote their positions as $$(A, B) = (\{\}, \{\})$$, since the set of moves each player can make is empty.

An impartial game is one in which at any given point in the game, each player is allowed exactly the same set of moves. Normal-play nim is an example of an impartial game. In nim, there are one or more heaps of objects, and two players (we'll call them Alice and Bob), take turns choosing a heap and removing 1 or more objects from it. The winner is the player who removes the final object from the final heap. The game is impartial because for any given configuration of pile sizes, the moves Alice can make on her turn are exactly the same moves Bob would be allowed to make if it were his turn. In contrast, a game such as checkers is not impartial because, supposing Alice were playing red and Bob were playing black, for any given arrangement of pieces on the board, if it were Alice's turn, she would only be allowed to move the red pieces, and if it were Bob's turn, he would only be allowed to move the black pieces.

Note that any configuration of an impartial game can therefore be written as a single position, because the moves will be the same no matter whose turn it is. For example, the position of the zero game can simply be written $$\{\}$$, because if it's Alice's turn, she has no moves to make, and if it's Bob's turn, he has no moves to make either. A move can be associated with the position it leaves the next player in.

Doing so allows positions to be defined recursively. For example, consider the following game of Nim played by Alice and Bob.

Example Nim Game
Sizes of heaps Moves A B C 1 2 2          Alice takes 1 from A 0 2 2           Bob   takes 1 from B  0 1 2           Alice takes 1 from C  0 1 1           Bob   takes 1 from B  0 0 1           Alice takes 1 from C 0 0 0           Bob   has no moves, so Alice wins

\big\{*1, \{*1\}, *2\big\}, \big\{*2, \{*1, \{*1\},*2\} \big\}, \big\{\{*1\}, \{\{*1\}\}, \{*1, \{*1\}, *2\}\big\} \Big\}.$$
 * At step 6 of the game (when all of the heaps are empty) the position is $$\{\}$$, because Bob has no valid moves to make. We name this position $$*0$$.
 * At step 5, Alice had exactly one option: to remove one object from heap C, leaving Bob with no moves. Since her move leaves Bob in position $$*0$$, her position is written $$\{ *0 \}$$.  We name this position $$*1$$.
 * At step 4, Bob had two options: remove one from B or remove one from C. Note, however, that it didn't really matter which heap Bob removed the object from: Either way, Alice would be left with exactly one object in exactly one pile. So, using our recursive definition, Bob really only has one move: $$*1$$.   Thus, Bob's position is $$\{*1\}$$.
 * At step 3, Alice had 3 options: remove two from C, remove one from C, or remove one from B. Removing two from C leaves Bob in position $$*1$$.  Removing one from C leaves Bob with two piles, each of size one, i.e., position $$\{*1\}$$, as described in step 4. However, removing 1 from B would leave Bob with two objects in a single pile. His moves would then be $$*0$$ and  $$*1$$, so her move would result in the position $$\{*0, *1\}$$.  We call this position $$*2$$.  Alice's position is then the set of all her moves: $$\big\{*1, \{*1\}, *2\big\}$$.
 * Following the same recursive logic, at step 2, Bob's position is $$\big\{ \{*1, \{*1\}, *2\}, *2\big\}.$$
 * Finally, at step 1, Alice's position is $$\Big\{

Nimbers
The special names $$*0$$, $$*1$$, and $$*2$$ referenced in our example game are called nimbers. In general, the nimber $$*n$$ corresponds to the position in a game of nim where there are exactly $$n$$ objects in exactly one heap. Formally, nimbers are defined inductively as follows: $$*0$$ is $$\{\}$$, $$*1 = \{*0\}$$, $$*2 = \{*0, *1\}$$ and  for all $$n \geq 0$$, $$*(n+1) = *n \cup \{*n\}$$.

While the word nimber comes from the game nim, nimbers can be used to describe the positions of any finite, impartial game, and in fact, the Sprague–Grundy theorem states that every instance of a finite, impartial game can be associated with a single nimber.

Combining Games
Two games can be combined by adding their positions together. For example, consider another game of nim with heaps $$A'$$, $$B'$$, and $$C'$$.

Example Game 2
Sizes of heaps  Moves A' B' C' 1 1  1           Alice takes 1 from A' 0  1  1           Bob takes one from B' 0  0  1           Alice takes one from C' 0  0  0           Bob has no moves, so Alice wins.

We can combine it with our first example to get a combined game with six heaps: $$A$$, $$B$$, $$C$$, $$A'$$, $$B'$$, and $$C'$$:

Combined Game
Sizes of heaps   Moves A B  C  A' B' C'   1  2  2  1  1  1   Alice takes 1 from A 0  2  2  1  1  1   Bob takes 1 from A' 0  2  2  0  1  1   Alice takes 1 from B' 0  2  2  0  0  1   Bob takes 1 from C' 0  2  2  0  0  0   Alice takes 2 from B 0  0  2  0  0  0   Bob takes 2 from C 0  0  0  0  0  0   Alice has no moves, so Bob wins.

To differentiate between the two games, for the first example game, we'll label its starting position $$\color{blue}S$$, and color it blue: $$\color{blue}S = \Big\{ \big\{*1, \{*1\}, *2\big\}, \big\{*2, \{*1, \{*1\},*2\} \big\}, \big\{\{*1\}, \{\{*1\}\}, \{*1, \{*1\}, *2\}\big\} \Big\}$$

For the second example game, we'll label the starting position $$\color{red}S'$$ and color it red: $$ \color{red}S' = \Big\{\{*1\}\Big\}. $$

To compute the starting position of the combined game, remember that a player can either make a move in the first game, leaving the second game untouched, or make a move in the second game, leaving the first game untouched. So the combined game's starting position is: $$ \color{blue}S \color{black} + \color{red}S' \color{black}= \Big\{ \color{blue}S\color{black} + \color{red} \{*1\} \color{black} \Big\} \cup \Big\{ \color{red}S'\color{black} + \color{blue}\{*1, \{*1\}, *2\} \color{black}, \color{red}S'\color{black} + \color{blue} \{*2, \{*1, \{*1\},*2\} \} \color{black}, \color{red}S'\color{black} + \color{blue} \{\{*1\}, \{\{*1\}\}, \{*1, \{*1\}, *2\}\} \color{black} \Big\} $$

The explicit formula for adding positions is: $$S+S'=\{S+s'\mid s'\in S'\}\cup\{s+S'\mid s\in S\}$$, which means that addition is both commutative and associative.

Equivalence
Positions in impartial games fall into two outcome classes: either the next player (the one whose turn it is) wins (an $$\boldsymbol{\mathcal{N}}$$- position), or the previous player wins (a $$\boldsymbol{\mathcal{P}}$$- position). So, for example, $$*0$$ is a $$\mathcal{P}$$-position, while $$*1$$ is an $$\mathcal{N}$$-position.

Two positions $$G$$ and $$G'$$ are equivalent if, no matter what position $$H$$ is added to them, they are always in the same outcome class. Formally, $$G \approx G' $$ if and only if $$\forall H $$, $$G + H$$ is in the same outcome class as $$G' + H$$.

To use our running examples, notice that in both the first and second games above, we can show that on every turn, Alice has a move that forces Bob into a $$\mathcal{P}$$-position. Thus, both $$\color{blue}S$$ and $$\color{red}S'$$ are $$\mathcal{N}$$-positions. (Notice that in the combined game, Bob is the player with the $$\mathcal{N}$$-positions. In fact, $$\color{blue}S \color{black} + \color{red}S' $$ is a $$\mathcal{P}$$-position, which as we will see in Lemma 2, means $$ \color{blue} S \color{black} \approx \color{red} S'$$.)

First Lemma
As an intermediate step to proving the main theorem, we show that for every position $$G$$ and every $$\mathcal{P}$$-position $$A$$, the equivalence $$G\approx A+G$$ holds. By the above definition of equivalence, this amounts to showing that $$G+H$$ and $$A+G+H$$ share an outcome class for all $$H$$.

Suppose that $$G+H$$ is a $$\mathcal{P}$$-position. Then the previous player has a winning strategy for $$A+G+H$$: respond to moves in $$A$$ according to their winning strategy for $$A$$ (which exists by virtue of $$A$$ being a $$\mathcal{P}$$-position), and respond to moves in $$G+H$$ according to their winning strategy for $$G+H$$ (which exists for the analogous reason). So $$A+G+H$$ must also be a $$\mathcal{P}$$-position.

On the other hand, if $$G+H$$ is an $$\mathcal{N}$$-position, then $$A+G+H$$ is also an $$\mathcal{N}$$-position, because the next player has a winning strategy: choose a $$\mathcal{P}$$-position from among the $$G+H$$ options, and we conclude from the previous paragraph that adding $$A$$ to that position is still a $$\mathcal{P}$$-position. Thus, in this case, $$A+G+H$$ must be a $$\mathcal{N}$$-position, just like $$G+H$$.

As these are the only two cases, the lemma holds.

Second Lemma
As a further step, we show that $$G\approx G'$$ if and only if $$G+G'$$ is a $$\mathcal{P}$$-position.

In the forward direction, suppose that $$G\approx G'$$. Applying the definition of equivalence with $$H=G$$, we find that $$G'+G$$ (which is equal to $$G+G'$$ by commutativity of addition) is in the same outcome class as $$G+G$$. But $$G+G$$ must be a $$\mathcal{P}$$-position: for every move made in one copy of $$G$$, the previous player can respond with the same move in the other copy, and so always make the last move.

In the reverse direction, since $$A=G+G'$$ is a $$\mathcal{P}$$-position by hypothesis, it follows from the first lemma, $$G\approx G+A$$, that $$G\approx G+(G+G')$$. Similarly, since $$B=G+G$$ is also a $$\mathcal{P}$$-position, it follows from the first lemma in the form $$G'\approx G'+B$$ that $$G'\approx G'+(G+G)$$. By associativity and commutativity, the right-hand sides of these results are equal. Furthermore, $$\approx$$ is an equivalence relation because equality is an equivalence relation on outcome classes. Via the transitivity of $$\approx$$, we can conclude that $$G\approx G'$$.

Proof
We prove that all positions are equivalent to a nimber by structural induction. The more specific result, that the given game's initial position must be equivalent to a nimber, shows that the game is itself equivalent to a nimber.

Consider a position $$G = \{G_1, G_2, \ldots, G_k\}$$. By the induction hypothesis, all of the options are equivalent to nimbers, say $$G_i \approx *n_i$$. So let $$G'=\{*n_1, *n_2, \ldots, *n_k\}$$. We will show that $$G \approx *m$$, where $$m$$ is the mex (minimum exclusion) of the numbers $$n_1, n_2, \ldots, n_k$$, that is, the smallest non-negative integer not equal to some $$n_i$$.

The first thing we need to note is that $$G \approx G'$$, by way of the second lemma. If $$k$$ is zero, the claim is trivially true. Otherwise, consider $$G+G'$$. If the next player makes a move to $$G_i$$ in $$G$$, then the previous player can move to $$*n_i$$ in $$G'$$, and conversely if the next player makes a move in $$G'$$. After this, the position is a $$\mathcal{P}$$-position by the lemma's forward implication. Therefore, $$G+G'$$ is a $$\mathcal{P}$$-position, and, citing the lemma's reverse implication, $$G \approx G'$$.

Now let us show that $$G'+*m$$ is a $$\mathcal{P}$$-position, which, using the second lemma once again, means that $$G'\approx *m$$. We do so by giving an explicit strategy for the previous player.

Suppose that $$G'$$ and $$*m$$ are empty. Then $$G'+*m$$ is the null set, clearly a $$\mathcal{P}$$-position.

Or consider the case that the next player moves in the component $$*m$$ to the option $$*m'$$ where $$m' m$$, the previous player moves in $$*n_i$$ to $$*m$$; in either case the result is a position plus itself. (It is not possible that $$n_i = m$$ because $$m$$ was defined to be different from all the $$n_i$$.)

In summary, we have $$G\approx G'$$ and $$G'\approx *m$$. By transitivity, we conclude that $$G \approx *m$$, as desired.

Development
If $$G$$ is a position of an impartial game, the unique integer $$m$$ such that $$G \approx *m$$ is called its Grundy value, or Grundy number, and the function that assigns this value to each such position is called the Sprague–Grundy function. R. L. Sprague and P. M. Grundy independently gave an explicit definition of this function, not based on any concept of equivalence to nim positions, and showed that it had the following properties: It follows straightforwardly from these results that if a position $$G$$ has a Grundy value of $$m$$, then $$G + H$$ has the same Grundy value as $$*m + H$$, and therefore belongs to the same outcome class, for any position $$H$$. Thus, although Sprague and Grundy never explicitly stated the theorem described in this article, it follows directly from their results and is credited to them. These results have subsequently been developed into the field of combinatorial game theory, notably by Richard Guy, Elwyn Berlekamp, John Horton Conway and others, where they are now encapsulated in the Sprague–Grundy theorem and its proof in the form described here. The field is presented in the books Winning Ways for your Mathematical Plays and On Numbers and Games.
 * The Grundy value of a single nim pile of size $$m$$ (i.e. of the position $$*m$$) is $$m$$;
 * A position is a loss for the next player to move (i.e. a $$\mathcal{P}$$-position) if and only if its Grundy value is zero; and
 * The Grundy value of the sum of a finite set of positions is just the nim-sum of the Grundy values of its summands.

title: Sprague–Grundy theorem


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Mode field diameter

In fiber optics, the mode field diameter (MFD) is a measure of the width of an irradiance distribution, i.e., the optical power per unit area, across the end face of a single-mode fiber. It is analogous to the $$1/e^2$$ measure of the beam diameter for a beam propagating in free space.

The mode field diameter is defined as twice the mode field radius, and the mode field radius is equal to the distance from the center at which the electric and magnetic field strengths are reduced to $$1/e$$ of their maximum values. Since the intensity (given by the Poynting vector) is proportional to the square of the field amplitude, the intensity drops by $$1/e^2 = 0.135$$ or -8.69 dB at this distance from the center. For a Gaussian-shaped mode, the mode field diameter is twice the beam waist $$w$$.

The MFD is typically slightly larger than the core of an optical fiber extending slightly into the cladding.

title: Mode field diameter


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Mode partition noise

Mode partition noise: In an optical communication link, is phase jitter of the signal caused by the combined effects of mode hopping in the optical source and intramodal distortion in the fiber.

Mode hopping causes random wavelength changes which in turn affect the group velocity, i.e., the propagation time. Over a long length of fiber, the cumulative effect is to create jitter, i.e. mode partition noise. The variation of group velocity creates the mode partition noise.

title: Mode partition noise


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Mode scrambler

In telecommunications, a mode scrambler or mode mixer is a device for inducing mode coupling in an optical fiber, or a device that, itself, exhibits a uniform output intensity profile independent of the input mode volume or modal excitation condition. Mode scramblers are used to provide a modal distribution that is independent of the optical source for purposes of laboratory, manufacturing, or field measurements or tests. Mode scramblers are primarily used to improve reproducibility of multimode fiber bandwidth measurements.

Overview
If multimode fiber bandwidth is measured using a laser diode directly coupled to its input, the resulting measurement can vary by as much as an order of magnitude. This measurement variability is due to the combination of differences in laser output characteristics (emitted mode power distribution) and the differential mode delay of the fiber. Differential mode delay is the difference in the time delays amongst the fiber's propagating modes caused by imperfections or nonideality of the fiber refractive index profile.

The primary purpose of a mode scrambler is to create a uniform, overfilled launch condition that can be easily reproduced on multiple measurement systems, so that measurement systems have essentially the same launch conditions and can measure approximately the same bandwidth despite having different laser sources. These were used for this purpose in the first U.S. NIST round-robins on multimode fiber. The overfilled launch (OFL) was created to reduce measurement variability, and improve concatenation estimates for multimode fibers, used at that time for telecom 'long haul' (e.g., 7–10 km 850 nm or 20–30 km 1300 nm) systems.

When the telecom industry converted to near-exclusive use of single-mode fiber ca. 1984, multimode fiber was re-purposed for use in LANs, such as Fiber Distributed Data Interface (FDDI), then under development. The output modal power distribution of a mode scrambler is similar to the surface-emitters used in those first LAN transmitters, but this was fortuitous coincidence. On average, but not in every case, the OFL bandwidth measured using a mode scrambler is lower than that produced by excitation of a partial mode volume (restricted mode launch or RML), such as occurs with directly coupled laser diodes.

Types
There are two common types of mode scramblers: the "Step-Graded-Step" (S-G-S) and the "step index with bends". The S-G-S mode scrambler is actually an assembly, a fusion-spliced concatenation of a step-index profile, a graded-index profile and another step-index profile fiber. Typically, each segment is approximately 1 meter long, and may use segments of unconventional size to produce the distribution required according to core size of fiber to be tested. Unconventional fiber size was not an issue, as they were developed by fiber manufacturers, but some test equipment has difficulty complying with revised qualification standards, and now use "Step Index with Bends" mode scramblers, which can be adjusted to purpose. Step Index with Bend mode scramblers are created simply by routing a specially designed step-index multimode fiber through a series of small radius bends, or by compressing fiber against surfaces with specific roughness. The implementations are simple, but generally less reproducible, and require care to avoid over-stressing the fiber.

A mode scrambler can be characterized and qualified by measuring its near-field and far-field distributions, as well as by measuring one of these distributions while restricting the other. Guidelines for constructing a mode scrambler and qualifying its output can be found in the ANSI/TIA/EIA-455-54 fiber optic test procedure (FOTP).

title: Mode scrambler


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Mode volume

In fiber optics, mode volume is the number of bound modes that an optical fiber is capable of supporting.

The mode volume M is approximately given by $$V^2 \over 2$$ and $${V^2 \over 2} \left({g \over g+2}\right)$$, respectively for step-index and power-law index profile fibers, where g is the profile parameter, and V is the normalized frequency, which must be greater than 5 for this approximation to be valid.

title: Mode volume


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Modification of Final Judgment

In United States telecommunication law, the Modification of Final Judgment (MFJ) is the August 1982 consent decree concerning the American Telephone and Telegraph Company (AT&T) and its subsidiaries, in the antitrust lawsuit United States v. AT&T of 1974. The terms required the Bell System divestiture, including removing local telephone service from AT&T control and placing business restrictions on the divested local telephone companies in exchange for removing other longstanding restrictions on what businesses AT&T could own and manage.

The decree replaced the entirety of the previous final judgment of January 24, 1956 in the case United States v. Western Electric Inc., which had been transferred to the United States District Court for the District of Columbia and is referred to in the MFJ as the Western Electric case, and consolidated with the existing United States v. AT&T filed on November 20, 1974, which is referred to in the MFJ as the AT&T action  or AT&T case.

The decree was made with Harold H. Greene as presiding judge.

title: Modification of Final Judgment


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Modified AMI code

Modified AMI codes are a digital telecommunications technique to maintain system synchronization. Alternate mark inversion (AMI) line codes are modified by deliberate insertion of bipolar violations. There are several types of modified AMI codes, used in various T-carrier and E-carrier systems.

Overview
The clock rate of an incoming T-carrier is extracted from its bipolar line code. Each signal transition provides an opportunity for the receiver to see the transmitter's clock. The AMI code guarantees that transitions are always present before and after each mark (1 bit), but are missing between adjacent spaces (0 bits). To prevent loss of synchronization when a long string of zeros is present in the payload, deliberate bipolar violations are inserted into the line code, to create a sufficient number of transitions to maintain synchronization; this is a form of run length limited coding. The receive terminal equipment recognizes the bipolar violations and removes from the user data the marks attributable to the bipolar violations.

T-carrier was originally developed for voice applications. When voice signals are digitized for transmission via T-carrier, the data stream always includes ample 1 bits to maintain synchronization. (To help this, the μ-law algorithm for digitizing voice signals encodes silence as a continuous stream of 1 bits.) However, when used for the transmission of digital data, the conventional AMI line code may fail to have sufficient marks to permit recovery of the incoming clock, and synchronization is lost. This happens when there are too many consecutive zeros in the user data being transported.

The exact pattern of bipolar violations that is transmitted in any given case depends on the line rate (i.e., the level of the line code in the T-carrier hierarchy) and the polarity of the last valid mark in the user data prior to the unacceptably long string of zeros. It would not be useful to have a violation immediately following a mark, as that would not produce a transition. For this reason, all modified AMI codes include a space (0 bit) before each violation mark.

In the descriptions below, "B" denotes a balancing mark with the opposite polarity to that of the preceding mark, while "V" denotes a bipolar violation mark, which has the same polarity as the preceding mark. In order to preserve AMI coding's desirable absence of DC bias, the number of positive marks must equal the number of negative marks. This happens automatically for balancing (B) marks, but the line code must ensure that positive and negative violation marks balance each other.

Zero length code suppression
The first technique used to ensure a minimum density of marks was zero code suppression a form of bit stuffing, which set the least significant bit of each 8-bit byte transmitted to a 1. (This bit was already unavailable due to robbed-bit signaling.) This avoided the need to modify the AMI code in any way, but limited available data rates to 56,000 bits per second per DS0 voice channel. Also, the low minimum density of ones (12.5%) sometimes led to increased clock slippage on the span.

Increased demand for bandwidth, and compatibility with the G.703 and ISDN PRI standards which called for 64,000 bits per second, led to this system being superseded by B8ZS.

B8ZS (North American T1)
Commonly used in the North American T1 (Digital Signal 1) 1.544 Mbit/s line code, bipolar with eight-zero substitution (B8ZS) replaces each string of 8 consecutive zeros with the special pattern "000VB0VB". Depending on the polarity of the preceding mark, that could be 000+−0−+ or 000−+0+−.

B6ZS (North American T2)
At the North American T2 rate (6.312 Mbit/s), bipolar violations are inserted if 6 or more consecutive zeros occur. This line code is called bipolar with six-zero substitution (B6ZS), and replaces 6 consecutive zeros with the pattern "0VB0VB". Depending on the polarity of the preceding mark, that could be 0+−0−+ or 0−+0+−.

HDB3 (European E-carrier)
Used in all levels of the European E-carrier system, the high density bipolar of order 3 (HDB3) code replaces any instance of 4 consecutive 0 bits with one of the patterns "000V" or "B00V". The choice is made to ensure that consecutive violations are of differing polarity; i.e., separated by an odd number of normal + or − marks.

These rules are applied on the code as it is being built from the original string. Every time there are 4 consecutive zeros in the code they will be replaced by either 000−, 000+, +00+ or −00−. To determine which pattern to use, one must count the number of pluses (+) and the number of minuses (−) since the last violation bit V, then subtract one from the other. If the result is an odd number then 000− or 000+ is used. If the result is an even number then +00+ or −00− is used. To determine which polarity to use, one must look at the pulse preceding the four zeros. If 000V form must be used then V simply copies the polarity of last pulse, if B00V form must be used then B and V chosen will have the opposite polarity of the last pulse.

Examples
Here are some examples of bit streams codes with AMI and HDB3. All assume the same starting conditions: the previous 1 bit was −, and the previous violation was an even number of 1 bits ago. (E.g. the preceding bits could have been ++−.)

B3ZS (North American T3)
At the North American T3 rate (44.736 Mbit/s), bipolar violations are inserted if 3 or more consecutive zeros occur. This line code is called bipolar with three-zero substitution (B3ZS), and is very similar to HDB3. Each run of 3 consecutive zeros is replaced by "00V" or "B0V". The choice is made to ensure that consecutive violations are of differing polarity, i.e. separated by an odd number of normal B marks.

title: Modified AMI code


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Μ-law algorithm

The μ-law algorithm (sometimes written mu-law, often approximated as u-law) is a companding algorithm, primarily used in 8-bit PCM digital telecommunication systems in North America and Japan. It is one of the two companding algorithms in the G.711 standard from ITU-T, the other being the similar A-law. A-law is used in regions where digital telecommunication signals are carried on E-1 circuits, e.g. Europe.

The terms PCMU, G711u or G711MU are used for G711 μ-law.

Companding algorithms reduce the dynamic range of an audio signal. In analog systems, this can increase the signal-to-noise ratio (SNR) achieved during transmission; in the digital domain, it can reduce the quantization error (hence increasing the signal-to-quantization-noise ratio). These SNR increases can be traded instead for reduced bandwidth for equivalent SNR.

At the cost of a reduced peak SNR, it can be mathematically shown that μ-law's non-linear quantization effectively increases dynamic range by 33 dB or $5 1⁄2$ bits over a linearly-quantized signal, hence 13.5 bits (which rounds up to 14 bits) is the most resolution required for an input digital signal to be compressed for 8-bit μ-law.

Algorithm types
The μ-law algorithm may be described in an analog form and in a quantized digital form.

Continuous

For a given input $x$, the equation for μ-law encoding is $$ F(x) = \sgn(x) \dfrac{\ln(1 + \mu |x|)}{\ln(1 + \mu)}, \quad -1 \leq x \leq 1, $$

where $μ = 255$ in the North American and Japanese standards, and $sgn(x)$ is the sign function. The range of this function is −1 to 1.

μ-law expansion is then given by the inverse equation: $$ F^{-1}(y) = \sgn(y) \dfrac{(1 + \mu)^{|y|} - 1}{\mu}, \quad -1 \leq y \leq 1. $$

Discrete
The discrete form is defined in ITU-T Recommendation G.711.

G.711 is unclear about how to code the values at the limit of a range (e.g. whether +31 codes to 0xEF or 0xF0). However, G.191 provides example code in the C language for a μ-law encoder. The difference between the positive and negative ranges, e.g. the negative range corresponding to +30 to +1 is −31 to −2. This is accounted for by the use of 1s' complement (simple bit inversion) rather than 2's complement to convert a negative value to a positive value during encoding.

Implementation
The μ-law algorithm may be implemented in several ways:
 * Analog: Use an amplifier with non-linear gain to achieve companding entirely in the analog domain.
 * Non-linear ADC: Use an analog-to-digital converter with quantization levels which are unequally spaced to match the μ-law algorithm.
 * Digital: Use the quantized digital version of the μ-law algorithm to convert data once it is in the digital domain.

 * Software/DSP
 * Use the continuous version of the μ-law algorithm to calculate the companded values.

Usage justification
μ-law encoding is used because speech has a wide dynamic range. In analog signal transmission, in the presence of relatively constant background noise, the finer detail is lost. Given that the precision of the detail is compromised anyway, and assuming that the signal is to be perceived as audio by a human, one can take advantage of the fact that the perceived acoustic intensity level or loudness is logarithmic by compressing the signal using a logarithmic-response operational amplifier (Weber–Fechner law). In telecommunications circuits, most of the noise is injected on the lines, thus after the compressor, the intended signal is perceived as significantly louder than the static, compared to an uncompressed source. This became a common solution, and thus, prior to common digital usage, the μ-law specification was developed to define an interoperable standard.

This pre-existing algorithm had the effect of significantly lowering the amount of bits required to encode a recognizable human voice in digital systems. A sample could be effectively encoded using μ-law in as little as 8 bits, which conveniently matched the symbol size of the majority of common computers.

μ-law encoding effectively reduced the dynamic range of the signal, thereby increasing the coding efficiency while biasing the signal in a way that results in a signal-to-distortion ratio that is greater than that obtained by linear encoding for a given number of bits.

The μ-law algorithm is also used in the .au format, which dates back at least to the SPARCstation 1 by Sun Microsystems as the native method used by the /dev/audio interface, widely used as a de facto standard for sound on Unix systems. The au format is also used in various common audio APIs such as the classes in the sun.audio Java package in Java 1.1 and in some C# methods.

This plot illustrates how μ-law concentrates sampling in the smaller (softer) values. The horizontal axis represents the byte values 0-255 and the vertical axis is the 16-bit linear decoded value of μ-law encoding.

Comparison with A-law
The μ-law algorithm provides a slightly larger dynamic range than the A-law at the cost of worse proportional distortions for small signals. By convention, A-law is used for an international connection if at least one country uses it.

title: Μ-law algorithm


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Multicast address

A multicast address is a logical identifier for a group of hosts in a computer network that are available to process datagrams or frames intended to be multicast for a designated network service. Multicast addressing can be used in the link layer (layer 2 in the OSI model), such as Ethernet multicast, and at the internet layer (layer 3 for OSI) for Internet Protocol Version 4 (IPv4) or Version 6 (IPv6) multicast.

IPv4
IPv4 multicast addresses are defined by the most-significant bit pattern of 1110. This originates from the classful network design of the early Internet when this group of addresses was designated as Class D. The CIDR notation for this group is. The group includes the addresses from to. Address assignments from within this range are specified in, an Internet Engineering Task Force (IETF) Best Current Practice document (BCP 51).

The address range is divided into blocks each assigned a specific purpose or behavior.

 * Local subnetwork
 * Addresses in the range of to  are individually assigned by IANA and designated for multicasting on the local subnetwork only. For example, the Routing Information Protocol (RIPv2) uses, Open Shortest Path First (OSPF) uses  and , and Multicast DNS uses . Routers must not forward these messages outside the subnet from which they originate.

 * Internetwork control block
 * Addresses in the range to  are individually assigned by IANA and designated as the internetwork control block. This block of addresses is used for traffic that must be routed through the public Internet, such as for applications of the Network Time Protocol using.

 * AD-HOC block
 * Addresses in three separate blocks are not individually assigned by IANA. These addresses are globally routed and are used for applications that don't fit either of the previously described purposes.

 * Source-specific multicast
 * The (IPv4) and  (IPv6) blocks are reserved for use by source-specific multicast.

 * GLOP
 * The range was originally assigned by  as an experimental, public statically-assigned multicast address space for publishers and Internet service providers that wished to source content on the Internet. The allocation method is termed GLOP addressing and provides implementers a block of 255 addresses that is determined by their 16-bit autonomous system number (ASN) allocation. In a nutshell, the middle two octets of this block are formed from assigned ASNs, giving any operator assigned an ASN 256 globally unique multicast group addresses. The method is not applicable to the newer 32-bit ASNs., superseding , envisioned the use of the range for many-to-many multicast applications. Unfortunately, with only 256 multicast addresses available to each autonomous system, GLOP is not adequate for large-scale broadcasters.

 * Unicast-prefix-based
 * The range is assigned by  as a range of global IPv4 multicast address space provided to each organization that has  or larger globally routed unicast address space allocated; one multicast address is reserved per  of unicast space. A resulting advantage over GLOP is that the unicast-prefix mechanism resembles the unicast-prefix capabilities of IPv6 as defined in.

 * Administratively scoped
 * The range is assigned by  for private use within an organization.  Per the RFC, packets destined to administratively scoped IPv4 multicast addresses do not cross administratively defined organizational boundaries, and administratively scoped IPv4 multicast addresses are locally assigned and do not have to be globally unique.  The RFC also discusses structuring the  range to be loosely similar to the scoped IPv6 multicast address range described in.

 * Ethernet-specific
 * In support of link-local multicasts which do not use IGMP, any IPv4 multicast address that falls within the and  ranges will be broadcast to all ports on many Ethernet switches, even if IGMP snooping is enabled, so addresses within these ranges should be avoided on Ethernet networks where the functionality of IGMP snooping is desired.

Notable IPv4 multicast addresses
The following table is a list of notable well-known IPv4 addresses that are reserved for IP multicasting and that are registered with the Internet Assigned Numbers Authority (IANA).

IPv6
Multicast addresses in IPv6 use the prefix. The general format of the IPv6 multicast address is described by RFC 4291:

Based on the value of the flag bits, IPv6 multicast addresses can be Unicast-Prefix-based Multicast Addresses, Source-Specific Multicast Addresses (both types introduced by RFC 3306, updated by RFC 7371), or Embedded RP IPv6 Multicast Addresses (introduced by RFC 3956, updated by RFC 7371). Each of these types of multicast addresses have their own format and follow specific rules.

Similar to a unicast address, the prefix of an IPv6 multicast address specifies its scope, however, the set of possible scopes for a multicast address is different. The 4-bit scope field (bits 12 to 15) is used to indicate where the address is valid and unique.

The service is identified in the group ID field. For example, if refers to all Network Time Protocol (NTP) servers on the local network segment, then  refers to all NTP servers in an organization's networks. The group ID field may be further divided for special multicast address types.

Notable IPv6 multicast addresses
The following table is a list notable IPv6 multicast addresses that are registered with IANA. To be included in some of the below multicast groups a client must send a Multicast Listener Discovery (MLD), a component of ICMPv6 suite, to join that group. For example, to listen to ff02::1:ff28:9c5a, a client must send a MLD report to the router, containing the multicast address, to indicate that it wants to listen to that group.

Ethernet
Ethernet frames with a value of 1 in the least-significant bit of the first octet of the destination MAC address are treated as multicast frames and are flooded to all points on the network. While frames with ones in all bits of the destination address are sometimes referred to as broadcasts, Ethernet generally does not distinguish between multicast and broadcast frames. Modern Ethernet controllers filter received packets to reduce CPU load, by looking up the hash of a multicast destination address in a table, initialized by software, which controls whether a multicast packet is dropped or fully received.

The IEEE has allocated the address block to  for group addresses for use by standard protocols. Of these, the MAC group addresses in the range of to  are not forwarded by 802.1D-conformant MAC bridges.

802.11
802.11 wireless networks use the same MAC addresses for multicast as Ethernet.

title: Multicast address