Trellis-coded Modulation
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Trellis-coded Modulation
In telecommunication, trellis modulation (also known as trellis coded modulation, or simply TCM) is a modulation scheme that transmits information with high efficiency over band-limited channels such as telephone lines. Gottfried Ungerboeck invented trellis modulation while working for IBM in the 1970s, and first described it in a conference paper in 1976. It went largely unnoticed, however, until he published a new, detailed exposition in 1982 that achieved sudden and widespread recognition. In the late 1980s, modems operating over plain old telephone service (''POTS'') typically achieved 9.6  kbit/s by employing four bits per symbol QAM modulation at 2,400 baud (symbols/second). This bit rate ceiling existed despite the best efforts of many researchers, and some engineers predicted that without a major upgrade of the public phone infrastructure, the maximum achievable rate for a POTS modem might be 14 kbit/s for two-way communication (3,429 baud × 4 bits/symbol, ...
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Telecommunication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that feasible with the human voice, but with a similar scale of expediency; thus, slow systems (such as postal mail) are excluded from the field. The transmission media in telecommunication have evolved through numerous stages of technology, from beacons and other visual signals (such as smoke signals, semaphore telegraphs, signal flags, and optical heliographs), to electrical cable and electromagnetic radiation, including light. Such transmission paths are often divided into communication channels, which afford the advantages of multiplexing multiple concurrent communication sessions. ''Telecommunication'' is often used in its plural form. Other examples of pre-modern long-distance communication included audio messages, such as coded drumb ...
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Telephone Line
A telephone line or telephone circuit (or just line or circuit industrywide) is a single-user circuit on a telephone communication system. It is designed to reproduce speech of a quality that is understandable. It is the physical wire or other signaling medium connecting the user's telephone apparatus to the telecommunications network, and usually also implies a single telephone number for billing purposes reserved for that user. Telephone lines are used to deliver landline telephone service and Digital subscriber line (DSL) phone cable service to the premises. Telephone overhead lines are connected to the public switched telephone network. The voltage at a subscriber's network interface is typically 48 V between the ring and tip wires, with tip near ground and ring at -48 V. In the United States In 1878, the Bell Telephone Company began to use two-wire circuits, called the local loop, from each user's telephone to end offices which performed any necessary electrical s ...
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Gottfried Ungerboeck
Gottfried Ungerboeck (born 15 March 1940, Vienna) is an Austrian communications engineer. Ungerboeck received an electrical engineering degree (with emphasis on telecommunications) from Vienna University of Technology in 1964, and a Ph.D. from the Swiss Federal Institute of Technology, Zurich, in 1970. He joined IBM Austria as a systems engineer in 1965, and the IBM Zurich Research Laboratory in 1967. At Zurich he worked on digital signal processing and switching systems, communication and information theory. Among many contributions to the theory of data transmission, he invented trellis coded modulation. Ungerboeck joined Broadcom in 1998 as Technical Director for Communication business line. He has won the 2018 Shannon Award of the IEEE Information Theory Society. Awards and honours *IBM Fellow (1984) *IEEE Fellow (1985) *Broadcom Fellow and Distinguished Engineer (2006) *IEEE Richard W. Hamming Medal (1994) *Marconi Prize (1996) * Australia Prize (1997) * Golden Jubile ...
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Modem
A modulator-demodulator or modem is a computer hardware device that converts data from a digital format into a format suitable for an analog transmission medium such as telephone or radio. A modem transmits data by Modulation#Digital modulation methods, modulating one or more carrier wave signals to encode digital information, while the receiver Demodulation, demodulates the signal to recreate the original digital information. The goal is to produce a Signal (electronics), signal that can be transmitted easily and decoded reliably. Modems can be used with almost any means of transmitting analog signals, from light-emitting diodes to radio. Early modems were devices that used audible sounds suitable for transmission over traditional telephone systems and leased lines. These generally operated at 110 or 300 bits per second (bit/s), and the connection between devices was normally manual, using an attached telephone handset. By the 1970s, higher speeds of 1,200 and 2,400  ...
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Plain Old Telephone Service
Plain old telephone service (POTS), or plain ordinary telephone system, is a retronym for voice-grade telephone service employing analog signal transmission over copper loops. POTS was the standard service offering from telephone companies from 1876 until 1988 in the United States when the Integrated Services Digital Network (ISDN) Basic Rate Interface (BRI) was introduced, followed by cellular telephone systems, and voice over IP (VoIP). POTS remains the basic form of residential and small business service connection to the telephone network in many parts of the world. The term reflects the technology that has been available since the introduction of the public telephone system in the late 19th century, in a form mostly unchanged despite the introduction of Touch-Tone dialing, electronic telephone exchanges and fiber-optic communication into the public switched telephone network (PSTN). Characteristics POTS is characterized by several aspects: *Bi-directional (full duplex) comm ...
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Kbit/s
In telecommunications, data-transfer rate is the average number of bits (bitrate), characters or symbols (baudrate), or data blocks per unit time passing through a communication link in a data-transmission system. Common data rate units are multiples of bits per second (bit/s) and bytes per second (B/s). For example, the data rates of modern residential high-speed Internet connections are commonly expressed in megabits per second (Mbit/s). Standards for unit symbols and prefixes Unit symbol The ISQ symbols for the bit and byte are ''bit'' and ''B'', respectively. In the context of data-rate units, one byte consists of 8 bits, and is synonymous with the unit octet. The abbreviation bps is often used to mean bit/s, so that when a ''1 Mbps'' connection is advertised, it usually means that the maximum achievable bandwidth is 1 Mbit/s (one million bits per second), which is 0.125 MB/s (megabyte per second), or about 0.1192 MiB/s (mebibyte per second). The Institu ...
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Quadrature Amplitude Modulation
Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signals, or two digital bit streams, by changing (''modulating'') the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves are of the same frequency and are out of phase with each other by 90°, a condition known as orthogonality or quadrature. The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality property. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the narrowband assumption. Phase modulation (analog PM) ...
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Shannon's Theorem
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel. This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley. The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data transmission errors, for a particular noise level. It was first described by Shannon (1948), and shortly after published in a book by Shannon and Warren Weaver entitled ''The Mathematical Theory of Communication'' (1949). This founded the modern discipline of information theory. Overview Stated by Claude Shanno ...
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Garden Trellis
A trellis (treillage) is an architectural structure, usually made from an open framework or lattice of interwoven or intersecting pieces of wood, bamboo or metal that is normally made to support and display climbing plants, especially shrubs.The Book of Garden Furniture
C. Thonger, 1903


Types

There are many types of trellis for different places and for different plants, from agricultural types, especially in , which are covered at , to garden uses for climbers such as

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Convolutional Code
In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity. The ability to perform economical maximum likelihood soft decision decoding is one of the major benefits of convolutional codes. This is in contrast to classic block codes, which are generally represented by a time-variant trellis and therefore are typically hard-decision decoded. Convolutional codes are often characterized by the base code rate and the depth (or memory) of the encoder ,k,K/math>. The base code rate is ty ...
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Symbol (data)
In a digitally modulated signal or a line code, symbol rate, modulation rate or baud rate is the number of symbol changes, waveform changes, or signaling events across the transmission medium per unit of time. The symbol rate is measured in ''baud'' (Bd) or ''symbols per second''. In the case of a line code, the symbol rate is the pulse rate in pulses per second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to the ''gross bit rate'', expressed in ''bits per second''. Symbols A symbol may be described as either a pulse in digital baseband transmission or a tone in passband transmission using modems. A symbol is a waveform, a state or a significant condition of the communication channel that ''persists'', for a fixed period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. The ...
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