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Channel Coding
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for error control, controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a Redundancy (information theory), redundant way, most often by using an error correction code, or error correcting code (ECC). The redundancy allows the receiver not only to error detection, detect errors that may occur anywhere in the message, but often to correct a limited number of errors. Therefore a reverse channel to request re-transmission may not be needed. The cost is a fixed, higher forward channel bandwidth. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communic ...
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Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both computer hardware, hardware and software. Computing has scientific, engineering, mathematical, technological, and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology, and software engineering. The term ''computing'' is also synonymous with counting and calculation, calculating. In earlier times, it was used in reference to the action performed by Mechanical computer, mechanical computing machines, and before that, to Computer (occupation), human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. ...
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Cellular Network
A cellular network or mobile network is a telecommunications network where the link to and from end nodes is wireless network, wireless and the network is distributed over land areas called ''cells'', each served by at least one fixed-location transceiver (such as a base station). These base stations provide the cell with the network coverage which can be used for transmission of voice, data, and other types of content via radio waves. Each cell's coverage area is determined by factors such as the power of the transceiver, the terrain, and the frequency band being used. A cell typically uses a different set of frequencies from neighboring cells, to avoid interference and provide guaranteed service quality within each cell. When joined together, these cells provide radio coverage over a wide geographic area. This enables numerous Mobile device, devices, including mobile phones, Tablet computer, tablets, laptops equipped with mobile broadband modems, and Wearable technology, wea ...
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Systematic Code
In coding theory, a systematic code is any error-correcting code in which the input data are embedded in the encoded output. Conversely, in a non-systematic code the output does not contain the input symbols. Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do not need to recover the original source symbols if received correctly – this is useful for example if error-correction coding is combined with a hash function for quickly determining the correctness of the received source symbols, or in cases where errors occur in erasures and a received symbol is thus always correct. Furthermore, for engineering purposes such as synchronization and monitoring, it is desirable to get reasonable good estimates of the received source symbols without going through the lengthy decoding process which may be carried out at a remote site at a later time. Properties Every non-systematic linear code can be transformed into a syst ...
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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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Polar Code (coding Theory)
In information theory, polar codes are a linear block error-correcting codes. The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels. When the number of recursions becomes large, the virtual channels tend to either have high reliability or low reliability (in other words, they polarize or become sparse), and the data bits are allocated to the most reliable channels. It is the first code with an explicit construction to provably achieve the channel capacity for symmetric binary-input, discrete, memoryless channels (B-DMC) with polynomial dependence on the gap to capacity. Polar codes were developed by Erdal Arikan, a professor of electrical engineering at Bilkent University. Notably, polar codes have modest encoding and decoding complexity , which renders them attractive for many applications. Moreover, the encoding and decoding energy complexity of generalized polar codes can ...
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Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist, cryptographer and inventor known as the "father of information theory" and the man who laid the foundations of the Information Age. Shannon was the first to describe the use of Boolean algebra—essential to all digital electronic circuits—and helped found artificial intelligence (AI). Roboticist Rodney Brooks declared Shannon the 20th century engineer who contributed the most to 21st century technologies, and mathematician Solomon W. Golomb described his intellectual achievement as "one of the greatest of the twentieth century". At the University of Michigan, Shannon dual degreed, graduating with a Bachelor of Science in electrical engineering and another in mathematics, both in 1936. A 21-year-old master's degree student in electrical engineering at MIT, his thesis, "A Symbolic Analysis of Relay and Switching Circuits", demonstrated that electric ...
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Noisy-channel Coding 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 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 C ...
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Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as communication systems, audio systems, radar systems, imaging systems, and data acquisition systems. A high SNR means that the signal is clear and easy to detect or interpret, while a low SNR means that the signal is corrupted or obscured by noise and may be difficult to distinguish or recover. SNR can be improved by various methods, such as increasing the signal strength, reducing the noise level, filtering out unwanted noise, or using error correction techniques. SNR also determines the maximum possible amount of data that ...
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Computer Memory
Computer memory stores information, such as data and programs, for immediate use in the computer. The term ''memory'' is often synonymous with the terms ''RAM,'' ''main memory,'' or ''primary storage.'' Archaic synonyms for main memory include ''core'' (for magnetic core memory) and ''store''. Main memory operates at a high speed compared to mass storage which is slower but less expensive per bit and higher in capacity. Besides storing opened programs and data being actively processed, computer memory serves as a Page cache, mass storage cache and write buffer to improve both reading and writing performance. Operating systems borrow RAM capacity for caching so long as it is not needed by running software. If needed, contents of the computer memory can be transferred to storage; a common way of doing this is through a memory management technique called ''virtual memory''. Modern computer memory is implemented as semiconductor memory, where data is stored within memory cell (com ...
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ECC Memory
Error correction code memory (ECC memory) is a type of computer data storage that uses an error correction code (ECC) to detect and correct ''n''-bit data corruption which occurs in memory. Typically, ECC memory maintains a memory system immune to single-bit errors: the data that is read from each word is always the same as the data that had been written to it, even if one of the bits actually stored has been flipped to the wrong state. Most non-ECC memory cannot detect errors, although some non-ECC memory with parity support allows detection but not correction. ECC memory is used in most computers where data corruption cannot be tolerated, like industrial control applications, critical databases, and infrastructural memory caches. Concept Error correction codes protect against undetected data corruption and are used in computers where such corruption is unacceptable, examples being scientific and financial computing applications, or in database and file servers. ECC can a ...
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Mass Storage
In computing, mass storage refers to the storage of large amounts of data in a persisting and machine-readable fashion. In general, the term ''mass'' in ''mass storage'' is used to mean ''large'' in relation to contemporaneous hard disk drives, but it has also been used to mean ''large'' relative to the size of primary memory as for example with floppy disks on personal computers. Devices and/or systems that have been described as mass storage include tape libraries, RAID systems, and a variety of computer drives such as hard disk drives (HDDs), magnetic tape drives, magneto-optical disc drives, optical disc drives, memory cards, and solid-state drives (SSDs). It also includes experimental forms like holographic memory. Mass storage includes devices with removable and non-removable media. It does not include random access memory (RAM). There are two broad classes of mass storage: local data in devices such as smartphones or computers, and enterprise servers and dat ...
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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 ...
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