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2B1Q
Two-binary, one-quaternary (2B1Q) is a line code used in the U interface of the Integrated Services Digital Network (ISDN) Basic Rate Interface (BRI) and the high-bit-rate digital subscriber line (HDSL). 2B1Q is a four-level pulse-amplitude modulation (PAM-4) scheme without redundancy, mapping two bits (2B) into one quaternary symbol (1Q). A competing encoding technique in the ISDN basic rate U interface, mainly used in Europe, is 4B3T. To minimize error propagation, bit pairs ( dibits) are assigned to voltage levels according to a Gray code, as follows: If the voltage is misread as an adjacent level, this causes only a 1-bit error in the decoded data. 2B1Q code is not DC-balanced In signal processing, when describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean amplitude of the waveform. If the mean amplitude is zero, there is no DC bias. A waveform with no DC .... Symbol rate is half of data rate. References ...
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High-bit-rate Digital Subscriber Line
High-bit-rate digital subscriber line (HDSL) is a telecommunications protocol standardized in 1994. It was the first digital subscriber line (DSL) technology to use a higher frequency spectrum over copper, twisted pair cables. HDSL was developed to transport DS1 services at 1.544 Mbit/s and 2.048 Mbit/s over telephone local loops without a need for repeaters. Successor technology to HDSL includes HDSL2 and HDSL4, proprietary SDSL, and G.SHDSL. Standardization HDSL was developed for T1 service at 1.544 Mbit/s by the American National Standards Institute (ANSI) Committee T1E1.4 and published in February 1994 as ANSI Technical Report TR-28. This American variant uses two wire pairs with at a rate of 784 kbit/s each, using the 2B1Q line code, which is also used in the American variant of the ISDN U interface. First products were developed in 1993. A European version of the standard for E1 service at 2.048 Mbit/s was published in February 1995 by the European Telecommuni ...
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Integrated Services Digital Network
Integrated Services Digital Network (ISDN) is a set of communication standards for simultaneous digital transmission of voice, video, data, and other network services over the digitalised circuits of the public switched telephone network. Work on the standard began in 1980 at Bell Labs and was formally standardized in 1988 in the CCITT "Red Book". By the time the standard was released, newer networking systems with much greater speeds were available, and ISDN saw relatively little uptake in the wider market. One estimate suggests ISDN use peaked at a worldwide total of 25 million subscribers at a time when 1.3 billion analog lines were in use. ISDN has largely been replaced with digital subscriber line (DSL) systems of much higher performance. Prior to ISDN, the telephone system consisted of digital links like T1/ E1 on the long-distance lines between telephone company offices and analog signals on copper telephone wires to the customers, the " last mile". At the time, t ...
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Line Code
In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems. Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably. Common line encodings are unipolar, polar, bipolar, and Manchester code. Transmission and storage After line coding, the signal is put through a physical communication channel, either a transmission medium or data storage medium.Karl Paulsen"Coding for Magnetic Storage Mediums".2007. The most common physical channels are: * the line-coded signal can directly be put on a transmission line, in the form of variations of the voltage or current (often using differential signaling). * the line-coded signal (the ''baseband signal'') underg ...
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Basic Rate Interface
Basic Rate Interface (BRI, 2B+D, 2B1D) or Basic Rate Access is an Integrated Services Digital Network (ISDN) configuration intended primarily for use in subscriber lines similar to those that have long been used for voice-grade telephone service. As such, an ISDN BRI connection can use the existing telephone infrastructure at a business. The BRI configuration provides 2 data (bearer) channels (B channels) at 64 kbit/s each and 1 control (delta) channel (D channel) at 16 kbit/s. The B channels are used for voice or user data, and the D channel is used for any combination of data, control/signaling, and X.25 packet networking. The 2 B channels can be aggregated by channel bonding providing a total data rate of 128 kbit/s. The BRI ISDN service is commonly installed for residential or small business service (ISDN PABX) in many countries. In contrast to the BRI, the Primary Rate Interface (PRI) configuration provides more B channels and operates at a higher bit rate. Physical i ...
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Quaternary Numeral System
A quaternary numeral system is base-. It uses the digits 0, 1, 2 and 3 to represent any real number. Conversion from binary is straightforward. Four is the largest number within the subitizing range and one of two numbers that is both a square and a highly composite number (the other being 36), making quaternary a convenient choice for a base at this scale. Despite being twice as large, its radix economy is equal to that of binary. However, it fares no better in the localization of prime numbers (the smallest better base being the primorial base six, senary). Quaternary shares with all fixed- radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers. See decimal and binary for a discussion of these properties. Relation to other positional number systems Relation to binary and hexadecimal As with the o ...
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4B3T
4B3T, which stands for 4 (four) binary 3 (three) ternary, is a line encoding scheme used for ISDN PRI interface. 4B3T represents four binary bits using three pulses. Description It uses three states: * + (positive pulse), * 0 (no pulse), and * − (negative pulse). This means we have 24 = 16 input combinations to represent, using 33 = 27 output combinations. 000 is not used to avoid long periods without a transition. 4B3T uses a paired disparity code to achieve an overall zero DC bias: six triplets are used which have no DC component (0+−, 0−+, +0−, −0+, +−0, −+0), and the remaining 20 are grouped into 10 pairs with differing disparity (e.g. ++− and −−+). When transmitting, the DC bias is tracked and a combination chosen that has a DC component of the opposite sign to the running total. This mapping from 4 bits to three ternary states is given in a table known as Modified Monitoring State 43 (MMS43). A competing encoding technique, used for the ISDN basic rate ...
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U Interface
U or u, is the twenty-first and sixth-to-last letter and fifth vowel letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''u'' (pronounced ), plural ''ues''. History U derives from the Semitic waw, as does F, and later, Y, W, and V. Its oldest ancestor goes to Egyptian hieroglyphics, and is probably from a hieroglyph of a mace or fowl, representing the sound v.html"_;"title="Voiced_labiodental_fricative.html"_;"title="nowiki/>Voiced_labiodental_fricative">v">Voiced_labiodental_fricative.html"_;"title="nowiki/>Voiced_labiodental_fricative">vor_the_sound_[Voiced_labial–velar_approximant.html" ;"title="Voiced_labiodental_fricative">v.html" ;"title="Voiced_labiodental_fricative.html" ;"title="nowiki/>Voiced labiodental fricative">v">Voiced_labiodental_fricative.html" ;"title="nowiki/>Voiced labiodental fricative">vor the sound [Voiced labial–velar approximant ...
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Pulse-amplitude Modulation
Pulse-amplitude modulation (PAM) is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. It is an analog pulse modulation scheme in which the amplitudes of a train of carrier pulses are varied according to the sample value of the message signal. Demodulation is performed by detecting the amplitude level of the carrier at every single period. Types There are two types of pulse amplitude modulation: * In ''single polarity PAM'', a suitable fixed DC bias is added to the signal to ensure that all the pulses are positive. * In ''double polarity PAM'', the pulses are both positive and negative. Pulse-amplitude modulation is widely used in modulating signal transmission of digital data, with non-baseband applications having been largely replaced by pulse-code modulation, and, more recently, by pulse-position modulation. The number of possible pulse amplitudes in analog PAM is theoretically infinite. Digital PAM reduces ...
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Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifica ...
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Error Propagation
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement limitations (e.g., instrument precision) which propagate due to the combination of variables in the function. The uncertainty ''u'' can be expressed in a number of ways. It may be defined by the absolute error . Uncertainties can also be defined by the relative error , which is usually written as a percentage. Most commonly, the uncertainty on a quantity is quantified in terms of the standard deviation, , which is the positive square root of the variance. The value of a quantity and its error are then expressed as an interval . If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the r ...
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Dibit
In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure information contained in messages and the entropy of random variables. The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes). Primary units In 1928, Ralph Hartley observed a fundamental storage principle, which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of ''N'' possible states of that system, denoted . Changing the base of the logarithm from ''b'' to a diff ...
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Gray Code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be "" and "2" would be "". In Gray code, these values are represented as "" and "". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. Motivation and name Many devices indicate position by closing and opening switches. If that device uses natural binary codes, positions 3 and 4 are next to each other but all three bits of the binary representation differ: : The problem with natural binary codes is that physical switches are not ideal ...
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