Space–time Trellis Code
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Space–time Trellis Code
Space–time trellis codes (STTCs) are a type of space–time code used in multiple-antenna wireless communications. This scheme transmits multiple, redundant copies of a generalised TCM signal distributed over time and a number of antennas ('space'). These multiple, 'diverse' copies of the data are used by the receiver to attempt to reconstruct the actual transmitted data. For an STC to be used, there must necessarily be multiple ''transmit'' antennas, but only a single ''receive'' antennas is required; nevertheless multiple receive antennas are often used since the performance of the system is improved by the resulting spatial diversity. In contrast to space–time block codes (STBCs), they are able to provide both coding gain and diversity gain and have a better bit-error rate performance. In essence they marry single channel continuous time coding with the signaling protocol being used, and extend that with a multi-antenna framework. However, that also means they are more com ...
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Space–time Code
A space–time code (STC) is a method employed to improve the reliability of data transmission (telecommunications), transmission in wireless, wireless communication systems using multiple transmit antenna (radio), antennas. STCs rely on transmitting multiple, redundancy (information theory), redundant copies of a data stream to the receiver (radio), receiver in the hope that at least some of them may survive the transmission medium, physical path between transmission and reception in a good enough state to allow reliable decoding. Space time codes may be split into two main types: *Space–time trellis codes (STTCs) distribute a convolutional code, trellis code over multiple antennas and multiple time-slots and provide both coding gain and diversity reception, diversity gain. *Space–time block codes (STBCs) act on a block of data at once (similarly to block codes) and also provide diversity reception, diversity gain but doesn't provide coding gain. *Space–time line codes ( ...
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Multiple-input Multiple-output
In radio, multiple-input and multiple-output (MIMO) () is a method for multiplying the capacity of a radio link using multiple transmission and receiving antennas to exploit multipath propagation. MIMO has become an essential element of wireless communication standards including IEEE 802.11n (Wi-Fi 4), IEEE 802.11ac (Wi-Fi 5), HSPA+ (3G), WiMAX, and Long Term Evolution (LTE). More recently, MIMO has been applied to power-line communication for three-wire installations as part of the ITU G.hn standard and of the HomePlug AV2 specification. At one time, in wireless the term "MIMO" referred to the use of multiple antennas at the transmitter and the receiver. In modern usage, "MIMO" specifically refers to a class of techniques for sending and receiving more than one data signal simultaneously over the same radio channel by exploiting the difference in signal propagation between different antennas (e.g. due to multipath propagation). Additionally, modern MIMO usage often refers t ...
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Wireless
Wireless communication (or just wireless, when the context allows) is the transfer of information (''telecommunication'') between two or more points without the use of an electrical conductor, optical fiber or other continuous guided transmission medium, medium for the transfer. The most common wireless technologies use radio waves. With radio waves, intended distances can be short, such as a few meters for Bluetooth, or as far as millions of kilometers for NASA Deep Space Network, deep-space radio communications. It encompasses various types of fixed, mobile, and portable applications, including two-way radios, Mobile phone, cellular telephones, personal digital assistants (PDAs), and wireless networking. Other examples of applications of radio ''wireless technology'' include Global Positioning System, GPS units, garage door openers, wireless Mouse (computing), computer mouse, Keyboard (computing), keyboards and Headset (audio), headsets, headphones, radio receivers, satelli ...
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Redundancy (information Theory)
Redundancy or redundant may refer to: Language * Redundancy (linguistics), information that is expressed more than once Engineering and computer science * Data redundancy, database systems which have a field that is repeated in two or more tables * Logic redundancy, a digital gate network containing circuitry that does not affect the static logic function * Redundancy (engineering), the duplication of critical components or functions of a system with the intention of increasing reliability * Redundancy (information theory), the number of bits used to transmit a message minus the number of bits of actual information in the message * Redundancy in total quality management, quality which exceeds the required quality level, creating unnecessarily high costs * The same task executed by several different methods in a user interface In the industrial design field of human–computer interaction, a user interface (UI) is the space where interactions between humans and machines o ...
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Trellis 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 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% of the theoretical maximum bit ...
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Antenna (radio)
In radio-frequency engineering, an antenna (American English) or aerial (British English) is an electronic device that converts an alternating current, alternating electric current into radio waves (transmitting), or radio waves into an electric current (receiving). It is the interface between radio waves Radio propagation, propagating through space and electric currents moving in metal Electrical conductor, conductors, used with a transmitter or receiver (radio), receiver. In transmission (telecommunications), transmission, a radio transmitter supplies an electric current to the antenna's Terminal (electronics), terminals, and the antenna radiates the energy from the current as electromagnetic radiation, electromagnetic waves (radio waves). In receiver (radio), reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplifier, amplified. Antennas are essential components ...
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Space–time Block Code
Space–time block coding is a technique used in wireless, wireless communications to transmit multiple copies of a data stream across a number of Antenna (radio), antennas and to exploit the various received versions of the data to improve the reliability of data transfer. The fact that the transmitted signal must traverse a potentially difficult environment with scattering, Reflection (physics), reflection, refraction and so on and may then be further corrupted by thermal noise in the Receiver (radio), receiver means that some of the received copies of the data may be closer to the original signal than others. This redundancy results in a higher chance of being able to use one or more of the received copies to correctly decode the received signal. In fact, Space–time code, space–time coding combines ''all'' the copies of the received signal in an optimal way to extract as much information from each of them as possible. Introduction Most work on wireless communications until ...
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Bit Error Rate
In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors. The bit error rate (BER) is the number of bit errors per unit time. The bit error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. Bit error ratio is a unitless performance measure, often expressed as a percentage. The bit error probability ''pe'' is the expected value of the bit error ratio. The bit error ratio can be considered as an approximate estimate of the bit error probability. This estimate is accurate for a long time interval and a high number of bit errors. Example As an example, assume this transmitted bit sequence: 1 1 0 0 0 1 0 1 1 and the following received bit sequence: 0 1 0 1 0 1 0 0 1, The number of bit errors (the underlined bits) is, in this case, 3. The BER is 3 ...
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Viterbi Algorithm
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events. This is done especially in the context of Markov information sources and hidden Markov models (HMM). The algorithm has found universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, satellite, deep-space communications, and 802.11 wireless LANs. It is now also commonly used in speech recognition, speech synthesis, diarization, keyword spotting, computational linguistics, and bioinformatics. For example, in speech-to-text (speech recognition), the acoustic signal is treated as the observed sequence of events, and a string of text is considered to be the "hidden cause" of the acoustic signal. The Viterbi algorithm finds the most likely string of text given the acoustic signal. His ...
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Linear
In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x)=(ax,bx) that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables X, Y and Z is aX+bY+cZ+d. Linearity of a mapping is closely related to '' proportionality''. Examples in physics include the linear relationship of voltage and current in an electrical conductor ( Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are '' nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. Linearity of a polynomial means that its de ...
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Vahid Tarokh
Vahid Tarokh (; born ) is an Iranian–American electrical engineer, mathematician, computer scientist, and professor. Since 2018, he has served as a Professor of Electrical and Computer Engineering, a Professor of Mathematics, and the Rhodes Family Professor of Electrical and Computer Engineering at Duke University. From 2019 to 2021, he was a Microsoft Data Science Investigator at Microsoft Innovation Hub at Duke University. Tarokh works with complex datasets and uses machine learning algorithms to predict catastrophic events. Biography Vahid Tarokh was born in the Imperial State of Iran. He received the M.Sc. degree in Mathematics from University of Windsor, Ontario, Canada in 1992, and the PhD in Electrical Engineering from the University of Waterloo, Ontario, Canada in 1995. At the University of Waterloo, he studied under Ian Fraser Blake, who also served as his Ph.D. advisor; his dissertation was titled ''Trellis Complexity of Lattices'' (1995). He worked at AT&T Labs-Resea ...
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