Trellis-coded Modulation
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Trellis-coded Modulation
Trellis coded modulation (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 quadrature amplitude modulation, 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, using QAM). 14 kbit/s is only 40% ...
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Modulation
Signal modulation is the process of varying one or more properties of a periodic waveform in electronics and telecommunication for the purpose of transmitting information. The process encodes information in form of the modulation or message signal onto a carrier signal to be transmitted. For example, the message signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer. This carrier wave usually has a much higher frequency than the message signal does. This is because it is impractical to transmit signals with low frequencies. Generally, receiving a radio wave requires a radio antenna with a length that is one-fourth of the wavelength of the transmitted wave. For low frequency radio waves, wavelength is on the scale of kilometers and building such a large antenna is not practical. Another purpose of modulation ...
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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 consistent 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 using two-wire circuits, called the local loop, from each user's telephone to end offices, which performed a ...
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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 Broadcom Inc. is an American multinational corporation, multinational designer, developer, manufacturer, and global supplier of a wide range of semiconductor and infrastructure software products. Broadcom's product offerings serve the data cen ... in 1998, as Technical Director for Communication business line. He has won the 2018 Shannon ...
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Modem
The Democratic Movement (, ; MoDem ) is a centre to centre-right political party in France, whose main ideological trends are liberalism and Christian democracy, and that is characterised by a strong pro-Europeanist stance. MoDem was established by François Bayrou to succeed the Union for French Democracy (UDF) and contest the 2007 legislative election, after his strong showing in the 2007 presidential election. Initially named the Democratic Party (''Parti démocrate''), the party was renamed "Democratic Movement", because there was already a small Democratic Party in France. MoDem secured an agreement with La République En Marche! (LRM) — later Renaissance (RE) — in the 2017 legislative election after Bayrou had endorsed the candidacy of Emmanuel Macron in February. The two parties have since been in alliance, as of late named Ensemble. The party's founder and leader Bayrou has served as Prime Minister of France since December 2024. History Background MoDem tr ...
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Plain Old Telephone Service
Plain old telephone service (POTS), or publicly offered telephone service, is basic Voice band, voice-grade telephone service. Historically, POTS has been delivered by Analog signal, analog signal transmission over copper loops, but the term also describes Backward compatibility, backward-compatible analog connections offered by digital telephone systems. Copper loop POTS was the standard service offering from telephone companies in the United States from 1876 until 1988, when the Integrated Services Digital Network (ISDN) Basic Rate Interface (BRI) was introduced, followed by the development of mobile phone, cellular telephone systems and voice over internet protocol (VoIP). Despite the advent of these technologies, copper loop POTS remains a basic form of residential and small business connection to the telephone network in many parts of the world. The term encapsulates a technology that has been available since the introduction of the public telephone system in the late 19th c ...
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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). ...
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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 phase, 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. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the In-phase and quadrature components#Narrowband ...
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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 (in theory) 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 Code rate, 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 State ...
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Garden Trellis
A trellis (French: ''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 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. There ...
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