Telecommunication is the transmission of signs, messages, writings and sounds or information of any nature by wire, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology, it is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are divided into communication channels which afford the advantages of multiplexing. Since the Latin term communicatio is considered the social process of information exchange, the term telecommunications is used in its plural form because it involves many different technologies. Early means of communicating over a distance included visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, optical heliographs. Other examples of pre-modern long-distance communication included audio messages such as coded drumbeats, lung-blown horns, loud whistles. 20th- and 21st-century technologies for long-distance communication involve electrical and electromagnetic technologies, such as telegraph and teleprinter, radio, microwave transmission, fiber optics, communications satellites.
A revolution in wireless communication began in the first decade of the 20th century with the pioneering developments in radio communications by Guglielmo Marconi, who won the Nobel Prize in Physics in 1909, other notable pioneering inventors and developers in the field of electrical and electronic telecommunications. These included Charles Wheatstone and Samuel Morse, Alexander Graham Bell, Edwin Armstrong and Lee de Forest, as well as Vladimir K. Zworykin, John Logie Baird and Philo Farnsworth; the word telecommunication is a compound of the Greek prefix tele, meaning distant, far off, or afar, the Latin communicare, meaning to share. Its modern use is adapted from the French, because its written use was recorded in 1904 by the French engineer and novelist Édouard Estaunié. Communication was first used as an English word in the late 14th century, it comes from Old French comunicacion, from Latin communicationem, noun of action from past participle stem of communicare "to share, divide out.
Homing pigeons have been used throughout history by different cultures. Pigeon post had Persian roots, was used by the Romans to aid their military. Frontinus said; the Greeks conveyed the names of the victors at the Olympic Games to various cities using homing pigeons. In the early 19th century, the Dutch government used the system in Sumatra, and in 1849, Paul Julius Reuter started a pigeon service to fly stock prices between Aachen and Brussels, a service that operated for a year until the gap in the telegraph link was closed. In the Middle Ages, chains of beacons were used on hilltops as a means of relaying a signal. Beacon chains suffered the drawback that they could only pass a single bit of information, so the meaning of the message such as "the enemy has been sighted" had to be agreed upon in advance. One notable instance of their use was during the Spanish Armada, when a beacon chain relayed a signal from Plymouth to London. In 1792, Claude Chappe, a French engineer, built the first fixed visual telegraphy system between Lille and Paris.
However semaphore suffered from the need for skilled operators and expensive towers at intervals of ten to thirty kilometres. As a result of competition from the electrical telegraph, the last commercial line was abandoned in 1880. On 25 July 1837 the first commercial electrical telegraph was demonstrated by English inventor Sir William Fothergill Cooke, English scientist Sir Charles Wheatstone. Both inventors viewed their device as "an improvement to the electromagnetic telegraph" not as a new device. Samuel Morse independently developed a version of the electrical telegraph that he unsuccessfully demonstrated on 2 September 1837, his code was an important advance over Wheatstone's signaling method. The first transatlantic telegraph cable was completed on 27 July 1866, allowing transatlantic telecommunication for the first time; the conventional telephone was invented independently by Alexander Bell and Elisha Gray in 1876. Antonio Meucci invented the first device that allowed the electrical transmission of voice over a line in 1849.
However Meucci's device was of little practical value because it relied upon the electrophonic effect and thus required users to place the receiver in their mouth to "hear" what was being said. The first commercial telephone services were set-up in 1878 and 1879 on both sides of the Atlantic in the cities of New Haven and London. Starting in 1894, Italian inventor Guglielmo Marconi began developing a wireless communication using the newly discovered phenomenon of radio waves, showing by 1901 that they could be transmitted across the Atlantic Ocean; this was the start of wireless telegraphy by radio. Voice and music had little early success. World War I accelerated the development of radio for military communications. After the war, commercial radio AM broadcasting began in the 1920s and became an important mass medium for entertainment and news. World War II again accelerated development of radio for the wartime purposes of aircraft and land communication, radio navigation and radar. Development of stereo FM broadcasting of radio
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light and water waves; the law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection. In acoustics, reflection is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types besides visible light. Reflection of VHF and higher frequencies is important for radar. Hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors. Reflection of light is either diffuse depending on the nature of the interface. In specular reflection the phase of the reflected waves depends on the choice of the origin of coordinates, but the relative phase between s and p polarizations is fixed by the properties of the media and of the interface between them.
A mirror provides the most common model for specular light reflection, consists of a glass sheet with a metallic coating where the significant reflection occurs. Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths. Reflection occurs at the surface of transparent media, such as water or glass. In the diagram, a light ray PO strikes a vertical mirror at point O, the reflected ray is OQ. By projecting an imaginary line through point O perpendicular to the mirror, known as the normal, we can measure the angle of incidence, θi and the angle of reflection, θr; the law of reflection states that θi = θr, or in other words, the angle of incidence equals the angle of reflection. In fact, reflection of light may occur whenever light travels from a medium of a given refractive index into a medium with a different refractive index. In the most general case, a certain fraction of the light is reflected from the interface, the remainder is refracted. Solving Maxwell's equations for a light ray striking a boundary allows the derivation of the Fresnel equations, which can be used to predict how much of the light is reflected, how much is refracted in a given situation.
This is analogous to the way impedance mismatch in an electric circuit causes reflection of signals. Total internal reflection of light from a denser medium occurs if the angle of incidence is greater than the critical angle. Total internal reflection is used as a means of focusing waves that cannot be reflected by common means. X-ray telescopes are constructed by creating a converging "tunnel" for the waves; as the waves interact at low angle with the surface of this tunnel they are reflected toward the focus point. A conventional reflector would be useless as the X-rays would pass through the intended reflector; when light reflects off a material denser than the external medium, it undergoes a phase inversion. In contrast, a less dense, lower refractive index material will reflect light in phase; this is an important principle in the field of thin-film optics. Specular reflection forms images. Reflection from a flat surface forms a mirror image, which appears to be reversed from left to right because we compare the image we see to what we would see if we were rotated into the position of the image.
Specular reflection at a curved surface forms an image which may be demagnified. Such mirrors may have surfaces that are parabolic. If the reflecting surface is smooth, the reflection of light that occurs is called specular or regular reflection; the laws of reflection are as follows: The incident ray, the reflected ray and the normal to the reflection surface at the point of the incidence lie in the same plane. The angle which the incident ray makes with the normal is equal to the angle which the reflected ray makes to the same normal; the reflected ray and the incident ray are on the opposite sides of the normal. These three laws can all be derived from the Fresnel equations. In classical electrodynamics, light is considered as an electromagnetic wave, described by Maxwell's equations. Light waves incident on a material induce small oscillations of polarisation in the individual atoms, causing each particle to radiate a small secondary wave in all directions, like a dipole antenna. All these waves add up to give specular reflection and refraction, according to the Huygens–Fresnel principle.
In the case of dielectrics such as glass, the electric field of the light acts on the electrons in the material, the moving electrons generate fields and become new radiators. The refracted light in the glass is the combination of the forward radiation of the electrons and the incident light; the reflected light is the combination of the backward radiation of all of the electrons. In metals, electrons with no binding energy are called free electrons; when these electrons oscillate with the incident light, the phase difference between their radiation field and the incident field is π, so the forward radiation cancels the incident light, backward radiation is just the reflected light. Light–matter interaction in terms of photons is a topic of quantum electrodynamics, is described in detail by Richard Feynman in his popular book QED: The Strange Theory of Light and Matter; when light strikes the surface of a mate
In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies as it is produced by several different effects. In communication systems, noise is an error or undesired random disturbance of a useful information signal; the noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however distinguished from interference, for example in the signal-to-noise ratio, signal-to-interference ratio and signal-to-noise plus interference ratio measures. Noise is typically distinguished from distortion, an unwanted systematic alteration of the signal waveform by the communication equipment, for example in signal-to-noise and distortion ratio and total harmonic distortion plus noise measures. While noise is unwanted, it can serve a useful purpose in some applications, such as random number generation or dither. Different types of noise are generated by different processes. Thermal noise is unavoidable at non-zero temperature, while other types depend on device type or manufacturing quality and semiconductor defects, such as conductance fluctuations, including 1/f noise.
Johnson–Nyquist noise is unavoidable, generated by the random thermal motion of charge carriers, inside an electrical conductor, which happens regardless of any applied voltage. Thermal noise is white, meaning that its power spectral density is nearly equal throughout the frequency spectrum; the amplitude of the signal has nearly a Gaussian probability density function. A communication system affected by thermal noise is modeled as an additive white Gaussian noise channel. Shot noise in electronic devices results from unavoidable random statistical fluctuations of the electric current when the charge carriers traverse a gap. If electrons flow across a barrier they have discrete arrival times; those discrete arrivals exhibit shot noise. The barrier in a diode is used. Shot noise is similar to the noise created by rain falling on a tin roof; the flow of rain may be constant, but the individual raindrops arrive discretely. The root-mean-square value of the shot noise current in is given by the Schottky formula.
I n = 2 I q Δ B where I is the DC current, q is the charge of an electron, ΔB is the bandwidth in hertz. The Schottky formula assumes independent arrivals. Vacuum tubes exhibit shot noise because the electrons randomly leave the cathode and arrive at the anode. A tube may not exhibit the full shot noise effect: the presence of a space charge tends to smooth out the arrival times. Conductors and resistors do not exhibit shot noise because the electrons thermalize and move diffusively within the material. Shot noise has been demonstrated in mesoscopic resistors when the size of the resistive element becomes shorter than the electron–phonon scattering length. Flicker noise known as 1/f noise, is a signal or process with a frequency spectrum that falls off into the higher frequencies, with a pink spectrum, it occurs in all electronic devices and results from a variety of effects. Burst noise consists of sudden step-like transitions between two or more discrete voltage or current levels, as high as several hundred microvolts, at random and unpredictable times.
Each shift in offset voltage or current lasts for several milliseconds to seconds. It is known a popcorn noise for the popping or crackling sounds it produces in audio circuits. If the time taken by the electrons to travel from emitter to collector in a transistor becomes comparable to the period of the signal being amplified, that is, at frequencies above VHF and beyond, the transit-time effect takes place and noise input impedance of the transistor decreases. From the frequency at which this effect becomes significant, it increases with frequency and dominates other sources of noise. While noise may be generated in the electronic circuit itself, additional noise energy can be coupled into a circuit from the external environment, by inductive coupling or capacitive coupling, or through the antenna of a radio receiver. Intermodulation noise Caused. Crosstalk Phenomenon in which a signal transmitted in one circuit or channel of a transmission systems creates undesired interference onto a signal in another channel.
Interference Modification or disruption of a signal travelling along a mediumAtmospheric noise This noise is called static noise and it is the natural source of disturbance caused by lightning discharge in thunderstorm and the natural disturbances occurring in nature. Industrial noise Sources such as automobiles, ignition electric motors and switching gear, High voltage wires and fluorescent lamps cause industrial noise; these noises are produced by the discharge present in all these operations. Solar noise Noise that originates from the Sun is called solar noise. Under normal conditions there is constant radiation from the Sun due to its high temperature. Electrical disturbances such as corona discharges, as well as sunspots can produce additional noise; the intensity of solar noise varies over time in a solar cycle. Cosmic noise Distant stars generate. While these stars are too far away to individually affect
In physics refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most observed phenomenon, but other waves such as sound waves and water waves experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence θ1 and angle of refraction θ2 is equal to the ratio of phase velocities in the two media, or equivalently, to the indices of refraction of the two media. Sin θ 1 sin θ 2 = v 1 v 2 = n 2 n 1 Optical prisms and lenses utilize refraction to redirect light, as does the human eye; the refractive index of materials varies with the wavelength of light, thus the angle of the refraction varies correspondingly. This is called dispersion and causes prisms and rainbows to divide white light into its constituent spectral colors.
Consider a wave going from one material to another where its speed is slower as in the figure. If it reaches the interface between the materials at an angle one side of the wave will reach the second material first, therefore slow down earlier. With one side of the wave going slower the whole wave will pivot towards that side; this is why a wave will bend away from the surface or toward the normal when going into a slower material. In the opposite case of a wave reaching a material where the speed is higher, one side of the wave will speed up and the wave will pivot away from that side. Another way of understanding the same thing is to consider the change in wavelength at the interface; when the wave goes from one material to another where the wave has a different speed v, the frequency f of the wave will stay the same, but the distance between wavefronts or wavelength λ=v/f will change. If the speed is decreased, such as in the figure to the right, the wavelength will decrease. With an angle between the wave fronts and the interface and change in distance between the wave fronts the angle must change over the interface to keep the wave fronts intact.
From these considerations the relationship between the angle of incidence θ1, angle of transmission θ2 and the wave speeds v1 and v2 in the two materials can be derived. This is the law of refraction or Snell's law and can be written as sin θ 1 sin θ 2 = v 1 v 2; the phenomenon of refraction can in a more fundamental way be derived from the 2 or 3-dimensional wave equation. The boundary condition at the interface will require the tangential component of the wave vector to be identical on the two sides of the interface. Since the magnitude of the wave vector depend on the wave speed this requires a change in direction of the wave vector; the relevant wave speed in the discussion above is the phase velocity of the wave. This is close to the group velocity which can be seen as the truer speed of a wave, but when they differ it is important to use the phase velocity in all calculations relating to refraction. A wave traveling perpendicular to a boundary, i.e. having its wavefronts parallel to the boundary, will not change direction if the speed of the wave changes.
Refraction of light can be seen in many places in our everyday life. It makes objects under a water surface appear closer than they are, it is what optical lenses are based on, allowing for instruments such as glasses, binoculars and the human eye. Refraction is responsible for some natural optical phenomena including rainbows and mirages. For light, the refractive index n of a material is more used than the wave phase speed v in the material, they are, directly related through the speed of light in vacuum c as n = c v. In optics, the law of refraction is written as n 1 sin θ 1 = n 2 sin θ 2. Refraction occurs when light goes through a water surface since water has a refractive index of 1.33 and air has a refractive index of about 1. Looking at a straight object, such as a pencil in the figure here, placed at a slant in the water, the object appears to bend at the water's surface; this is due to the bending of light rays. Once the rays reach the eye, the eye traces them back as straight lines.
The lines of sight intersect at a higher position than. This causes the pencil to appear higher and the water to appear shallower than it is; the depth that the water appears to be when viewed from above is known as the apparent depth. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, the fisher must aim lower to catch the fish. Conversely
A communication channel or channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used to convey an information signal, for example a digital bit stream, from one or several senders to one or several receivers. A channel has a certain capacity for transmitting information measured by its bandwidth in Hz or its data rate in bits per second. Communicating data from one location to another requires some form of medium; these pathways, called communication channels, use two types of media: broadcast. Cable or wire line media use physical wires of cables to transmit data and information. Twisted-pair wire and coaxial cables are made of copper, fiber-optic cable is made of glass. In information theory, a channel refers to a theoretical channel model with certain error characteristics. In this more general view, a storage device is a kind of channel, which can be sent to and received from.
Examples of communications channels include: A connection between initiating and terminating nodes of a circuit. A single path provided by a transmission medium via either physical separation, such as by multipair cable or electrical separation, such as by frequency-division or time-division multiplexing. A path for conveying electrical or electromagnetic signals distinguished from other parallel paths. A storage which can communicate a message over time as well as space The portion of a storage medium, such as a track or band, accessible to a given reading or writing station or head. A buffer from which messages can be'put' and'got'. See Actor model and process calculi for discussion on the use of channels. In a communications system, the physical or logical link that connects a data source to a data sink. A specific radio frequency, pair or band of frequencies named with a letter, number, or codeword, allocated by international agreement. Examples: Marine VHF radio uses some 88 channels in the VHF band for two-way FM voice communication.
Channel 16, for example, is 156.800 MHz. In the US, seven additional channels, WX1 - WX7, are allocated for weather broadcasts. Television channels such as North American TV Channel 2 = 55.25 MHz, Channel 13 = 211.25 MHz. Each channel is 6 MHz wide; this was based on the bandwidth required by older analog television signals. Since 2006 television broadcasting has switched to digital modulation which uses image compression to transmit a television signal in a much smaller bandwidth, so each of these "physical channels" has been divided into multiple "virtual channels" each carrying a DTV channel. Wi-Fi uses 13 channels from 2412 MHz to 2484 MHz in 5 MHz steps, in the ISM bands; the radio channel between an amateur radio repeater and a ham uses two frequencies 600 kHz apart. For example, a repeater that transmits on 146.94 MHz listens for a ham transmitting on 146.34 MHz. All of these communications channels share the property; the information is carried through the channel by a signal. A channel can be modelled physically by trying to calculate the physical processes which modify the transmitted signal.
For example, in wireless communications the channel can be modelled by calculating the reflection off every object in the environment. A sequence of random numbers might be added in to simulate external interference and/or electronic noise in the receiver. Statistically a communication channel is modelled as a triple consisting of an input alphabet, an output alphabet, for each pair of input and output elements a transition probability p. Semantically, the transition probability is the probability that the symbol o is received given that i was transmitted over the channel. Statistical and physical modelling can be combined. For example, in wireless communications the channel is modelled by a random attenuation of the transmitted signal, followed by additive noise; the attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model electronic noise in the receiver. If the attenuation term is complex it describes the relative time a signal takes to get through the channel.
The statistics of the random attenuation are decided by previous measurements or physical simulations. Channel models may be continuous channel models in that there is no limit to how their values may be defined. Communication channels are studied in a discrete-alphabet setting; this corresponds to abstracting a real world communication system in which the analog → digital and digital → analog blocks are out of the control of the designer. The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory, it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input. A channel model may either be analog. In a digital channel model, the transmitted message is modelled as a digital signal at a certain protocol layer. Underlying protocol layers, such as the physical layer transmission technique, is replaced by a simplified model.
The model may reflect channel performance measures such as bit rate, bit errors, latency/delay, delay jitter, etc. Examples of digital channel models are: Binary symmetric channel, a discrete memoryless channel with a
Federal Communications Commission
The Federal Communications Commission is an independent agency of the United States government created by statute to regulate interstate communications by radio, wire and cable. The FCC serves the public in the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, homeland security; the FCC was formed by the Communications Act of 1934 to replace the radio regulation functions of the Federal Radio Commission. The FCC took over wire communication regulation from the Interstate Commerce Commission; the FCC's mandated jurisdiction covers the 50 states, the District of Columbia, the Territories of the United States. The FCC provides varied degrees of cooperation and leadership for similar communications bodies in other countries of North America; the FCC is funded by regulatory fees. It has an estimated fiscal-2016 budget of US $388 million, it has 1,688 federal employees, made up of 50% males and 50% females as of December, 2017. The FCC's mission, specified in Section One of the Communications Act of 1934 and amended by the Telecommunications Act of 1996 is to "make available so far as possible, to all the people of the United States, without discrimination on the basis of race, religion, national origin, or sex, efficient and world-wide wire and radio communication services with adequate facilities at reasonable charges."
The Act furthermore provides that the FCC was created "for the purpose of the national defense" and "for the purpose of promoting safety of life and property through the use of wire and radio communications."Consistent with the objectives of the Act as well as the 1999 Government Performance and Results Act, the FCC has identified four goals in its 2018-22 Strategic Plan. They are: Closing the Digital Divide, Promoting Innovation, Protecting Consumers & Public Safety, Reforming the FCC's Processes; the FCC is directed by five commissioners appointed by the President of the United States and confirmed by the United States Senate for five-year terms, except when filling an unexpired term. The U. S. President designates one of the commissioners to serve as chairman. Only three commissioners may be members of the same political party. None of them may have a financial interest in any FCC-related business. † Commissioners may continue serving until the appointment of their replacements. However, they may not serve beyond the end of the next session of Congress following term expiration.
In practice, this means that commissioners may serve up to 1 1/2 years beyond the official term expiration dates listed above if no replacement is appointed. This would end on the date that Congress adjourns its annual session no than noon on January 4; the FCC is organized into seven Bureaus, which process applications for licenses and other filings, analyze complaints, conduct investigations and implement regulations, participate in hearings. The Consumer & Governmental Affairs Bureau develops and implements the FCC's consumer policies, including disability access. CGB serves as the public face of the FCC through outreach and education, as well as through their Consumer Center, responsible for responding to consumer inquiries and complaints. CGB maintains collaborative partnerships with state and tribal governments in such areas as emergency preparedness and implementation of new technologies; the Enforcement Bureau is responsible for enforcement of provisions of the Communications Act 1934, FCC rules, FCC orders, terms and conditions of station authorizations.
Major areas of enforcement that are handled by the Enforcement Bureau are consumer protection, local competition, public safety, homeland security. The International Bureau develops international policies in telecommunications, such as coordination of frequency allocation and orbital assignments so as to minimize cases of international electromagnetic interference involving U. S. licensees. The International Bureau oversees FCC compliance with the international Radio Regulations and other international agreements; the Media Bureau develops and administers the policy and licensing programs relating to electronic media, including cable television, broadcast television, radio in the United States and its territories. The Media Bureau handles post-licensing matters regarding direct broadcast satellite service; the Wireless Telecommunications Bureau regulates domestic wireless telecommunications programs and policies, including licensing. The bureau implements competitive bidding for spectrum auctions and regulates wireless communications services including mobile phones, public safety, other commercial and private radio services.
The Wireline Competition Bureau develops policy concerning wire line telecommunications. The Wireline Competition Bureau's main objective is to promote growth and economical investments in wireline technology infrastructure, development and services; the Public Safety and Homeland Security Bureau was launched in 2006 with a focus on critical communications infrastructure. The FCC has eleven Staff Offices; the FCC's Offices provide support services to the Bureaus. The Office of Administrative Law Judges is responsible for conducting hearings ordered by the Commission; the hearing function includes acting on interlocutory requests filed in the proceedings such as petitions to intervene, petitions to enlarge issues, contested discovery requests. An Administrative Law Judge, appointed under the Administrative Procedure Act, presides at the hearing during which documents and sworn testimony are received in evidence, witnesses are cross-examined. At the co
The Viterbi algorithm is a dynamic programming algorithm for finding the most sequence of hidden states—called the Viterbi path—that results in a sequence of observed events in the context of Markov information sources and hidden Markov models. The algorithm has found universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, deep-space communications, 802.11 wireless LANs. It is now commonly used in speech recognition, speech synthesis, keyword spotting, computational linguistics, bioinformatics. For example, in speech-to-text, the acoustic signal is treated as the observed sequence of events, a string of text is considered to be the "hidden cause" of the acoustic signal; the Viterbi algorithm finds the most string of text given the acoustic signal. The Viterbi algorithm is named after Andrew Viterbi, who proposed it in 1967 as a decoding algorithm for convolutional codes over noisy digital communication links, it has, however, a history of multiple invention, with at least seven independent discoveries, including those by Viterbi and Wunsch, Wagner and Fischer."Viterbi path" and "Viterbi algorithm" have become standard terms for the application of dynamic programming algorithms to maximization problems involving probabilities.
For example, in statistical parsing a dynamic programming algorithm can be used to discover the single most context-free derivation of a string, called the "Viterbi parse". Another application is in target tracking, where the track is computed that assigns a maximum likelihood to a sequence of observations. A generalization of the Viterbi algorithm, termed the max-sum algorithm can be used to find the most assignment of all or some subset of latent variables in a large number of graphical models, e.g. Bayesian networks, Markov random fields and conditional random fields; the latent variables need in general to be connected in a way somewhat similar to an HMM, with a limited number of connections between variables and some type of linear structure among the variables. The general algorithm involves message passing and is similar to the belief propagation algorithm. With the algorithm called iterative Viterbi decoding one can find the subsequence of an observation that matches best to a given hidden Markov model.
This algorithm is proposed by Qi al. to deal with turbo code. Iterative Viterbi decoding works by iteratively invoking a modified Viterbi algorithm, reestimating the score for a filler until convergence. An alternative algorithm, the Lazy Viterbi algorithm, has been proposed. For many applications of practical interest, under reasonable noise conditions, the lazy decoder is much faster than the original Viterbi decoder. While the original Viterbi algorithm calculates every node in the trellis of possible outcomes, the Lazy Viterbi algorithm maintains a prioritized list of nodes to evaluate in order, the number of calculations required is fewer than the ordinary Viterbi algorithm for the same result. However, it is not so easy to parallelize in hardware; this algorithm generates a path X =, a sequence of states x n ∈ S = that generate the observations Y = with y n ∈ O =. Two 2-dimensional tables of size K × T are constructed: Each element T 1 of T 1 stores the probability of the most path so far X ^ = with x ^ j = s i that generates Y =.
Each element T 2 of T 2 stores x ^ j − 1 of the most path so far