Error 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). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.
Low-density parity-check codeIn information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of the bipartite graph). LDPC codes are , which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit) for a symmetric memoryless channel.
Turbo codeIn information theory, turbo codes (originally in French Turbocodes) 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. Turbo codes are used in 3G/4G mobile communications (e.g.
Noisy-channel coding theoremIn 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 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.
Integrated circuitAn integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of miniaturized transistors and other electronic components are integrated together on the chip. This results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete components, allowing a large transistor count.
Mixed-signal integrated circuitA mixed-signal integrated circuit is any integrated circuit that has both analog circuits and digital circuits on a single semiconductor die. Their usage has grown dramatically with the increased use of cell phones, telecommunications, portable electronics, and automobiles with electronics and digital sensors. Integrated circuits (ICs) are generally classified as digital (e.g. a microprocessor) or analog (e.g. an operational amplifier). Mixed-signal ICs contain both digital and analog circuitry on the same chip, and sometimes embedded software.
Error detection and correctionIn information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases.
Coding theoryCoding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods.
Erasure codeIn coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols. The fraction r = k/n is called the code rate. The fraction k’/k, where k’ denotes the number of symbols required for recovery, is called reception efficiency.
Decoding methodsIn coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel. is considered a binary code with the length ; shall be elements of ; and is the distance between those elements. One may be given the message , then ideal observer decoding generates the codeword .
Convolutional codeIn 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.
Integrated circuit designIntegrated circuit design, or IC design, is a sub-field of electronics engineering, encompassing the particular logic and circuit design techniques required to design integrated circuits, or ICs. ICs consist of miniaturized electronic components built into an electrical network on a monolithic semiconductor substrate by photolithography. IC design can be divided into the broad categories of digital and analog IC design. Digital IC design is to produce components such as microprocessors, FPGAs, memories (RAM, ROM, and flash) and digital ASICs.
Concatenated error correction codeIn coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived in 1966 by Dave Forney as a solution to the problem of finding a code that has both exponentially decreasing error probability with increasing block length and polynomial-time decoding complexity. Concatenated codes became widely used in space communications in the 1970s.
Tornado codeIn coding theory, Tornado codes are a class of erasure codes that support error correction. Tornado codes require a constant C more redundant blocks than the more data-efficient Reed–Solomon erasure codes, but are much faster to generate and can fix erasures faster. Software-based implementations of tornado codes are about 100 times faster on small lengths and about 10,000 times faster on larger lengths than Reed–Solomon erasure codes. Since the introduction of Tornado codes, many other similar erasure codes have emerged, most notably Online codes, LT codes and Raptor codes.
Block codeIn coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of all block codes in a unified way.
Linear integrated circuitA linear integrated circuit or analog chip is a set of miniature electronic analog circuits formed on a single piece of semiconductor material. The voltage and current at specified points in the circuits of analog chips vary continuously over time. In contrast, digital chips only assign meaning to voltages or currents at discrete levels. In addition to transistors, analog chips often include a larger number of passive elements (capacitors, resistors, and inductors) than digital chips.
Channel capacityChannel capacity, in electrical engineering, computer science, and information theory, is the tight upper bound on the rate at which information can be reliably transmitted over a communication channel. Following the terms of the noisy-channel coding theorem, the channel capacity of a given channel is the highest information rate (in units of information per unit time) that can be achieved with arbitrarily small error probability. Information theory, developed by Claude E.
Integrated circuit layout design protectionLayout designs (topographies) of integrated circuits are a field in the protection of intellectual property. In United States intellectual property law, a "mask work" is a two or three-dimensional layout or topography of an integrated circuit (IC or "chip"), i.e. the arrangement on a chip of semiconductor devices such as transistors and passive electronic components such as resistors and interconnections.
Hybrid integrated circuitA hybrid integrated circuit (HIC), hybrid microcircuit, hybrid circuit or simply hybrid is a miniaturized electronic circuit constructed of individual devices, such as semiconductor devices (e.g. transistors, diodes or monolithic ICs) and passive components (e.g. resistors, inductors, transformers, and capacitors), bonded to a substrate or printed circuit board (PCB). A PCB having components on a Printed Wiring Board (PWB) is not considered a true hybrid circuit according to the definition of MIL-PRF-38534.
Digital electronicsDigital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined.
