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Turbo code

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In information theory, turbo codes are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely approach the maximum channel capacity or Shannon limit, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.

Joachim HagenauerJoachim HagenauerJoachim Hagenauer (29 July 1941 – 16 January 2026) was a German information theorist and academic who was professor emeritus at Technical University of Munich. He pioneered the use of soft bits (see Soft output Viterbi algorithm), a coding theory technique that contributes to the high performance of the turbo codes. Hagenauer's work enabled the advancement of turbo coding and led to a significant improvement in channel coding for digital communications and storage.Low-density parity-check codeLow-density parity-check codeLow-density parity-check (LDPC) codes, also known as Gallager codes, are a class of error-correction codes first proposed in 1960. Together with the closely related turbo codes, they have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely used in applications ranging from wireless communications to flash-memory storage.Information theoryInformation theoryScientific study of digital informationInformation theory is the mathematical study of the quantification, storage, and communication of a particular type of mathematically defined information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley.Error correction codeError correction codeIn computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code, or error correcting code (ECC).Code rateCode rateIn telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is k/n{\displaystyle k/n}, for every k bits of useful information, the coder generates a total of n bits of data, of which n−k{\displaystyle n-k} are redundant.Shannon–Hartley theoremIn information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise.SatelliteSatelliteObjects intentionally placed into orbitTwo CubeSats orbiting around Earth after being deployed from the ISS Kibō module's Small Satellite Orbital DeployerA satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation (GPS), broadcasting, scientific research, and Earth observation.4G4G4G refers to the fourth generation of cellular network technology, introduced in the late 2000s and early 2010s. Compared to preceding third-generation (3G) technologies, 4G has been designed to support all-IP communications and broadband services, and eliminates circuit switching in voice telephony.3G3G3G is the third generation of cellular network technology. These networks were rolled out beginning in the early 2000s and represented a significant advancement over the second generation (2G) and associated technologies, such as GSM and cdmaOne, particularly in terms of data transfer speeds and mobile internet capabilities.LTE (telecommunication)In telecommunications, Long Term Evolution (LTE) is a standard for wireless broadband communication for cellular mobile devices and data terminals. It is considered to be a "transitional" 4G technology, and is therefore also referred to as 3.95G as a step above 3G. LTE is based on the 2G GSM/EDGE and 3G UMTS/HSPA standards. It improves on those standards' capacity and speed by using a different radio interface and core network improvements.UMTSUMTSThird generation mobile cellular system 3G sign shown in notification bar on an Android powered smartphone The Universal Mobile Telecommunications System (UMTS) is a 3G mobile cellular system for networks based on the GSM standard. UMTS uses wideband code-division multiple access (W-CDMA) radio access technology to offer greater spectral efficiency and bandwidth to mobile network operators compared to previous 2G systems like GPRS and CSD.TurbochargerTurbochargerIn an internal combustion engine, a turbocharger (also known as a turbo or, formerly, a turbosupercharger) is a forced induction device that compresses the intake air, forcing more air into the engine in order to produce more power for a given displacement.

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