In 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.
In Boolean logic, the majority function is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs. Representing true values as 1 and false values as 0, we may use the (real-valued) formula:
In 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.
A binary symmetric channel is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit, and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage.
Lempel–Ziv–Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published by Welch in 1984 as an improved implementation of the LZ78 algorithm published by Lempel and Ziv in 1978. The algorithm is simple to implement and has the potential for very high throughput in hardware implementations. It is the algorithm of the Unix file compression utility compress and is used in the GIF image format.
A satellite modem or satmodem is a modem used to establish data transfers using a communications satellite as a relay. A satellite modem's main function is to transform an input bitstream to a radio signal and vice versa.
Coding 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. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data.
The Lempel–Ziv–Markov chain algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under development since either 1996 or 1998 by Igor Pavlov and was first used in the 7z format of the 7-Zip archiver. This algorithm uses a dictionary compression scheme somewhat similar to the LZ77 algorithm published by Abraham Lempel and Jacob Ziv in 1977 and features a high compression ratio and a variable compression-dictionary size, while still maintaining decompression speed similar to other commonly used compression algorithms.
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. Turbo codes are used in 3G/4G mobile communications and in satellite communications as well as other applications where designers seek to achieve reliable information transfer over bandwidth- or latency-constrained communication links in the presence of data-corrupting noise. Turbo codes compete with low-density parity-check (LDPC) codes, which provide similar performance.
In 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. LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum for a symmetric memoryless channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear in their block length.
A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code.
In 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.
Leabra stands for local, error-driven and associative, biologically realistic algorithm. It is a model of learning which is a balance between Hebbian and error-driven learning with other network-derived characteristics. This model is used to mathematically predict outcomes based on inputs and previous learning influences. This model is heavily influenced by and contributes to neural network designs and models. This algorithm is the default algorithm in emergent when making a new project, and is extensively used in various simulations.
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.
In computing, triple modular redundancy, sometimes called triple-mode redundancy, (TMR) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produce a single output. If any one of the three systems fails, the other two systems can correct and mask the fault.
In 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.
In coding theory, list decoding is an alternative to unique decoding of error-correcting codes for large error rates. The notion was proposed by Elias in the 1950s. The main idea behind list decoding is that the decoding algorithm instead of outputting a single possible message outputs a list of possibilities one of which is correct. This allows for handling a greater number of errors than that allowed by unique decoding.
G.718 is an ITU-T Recommendation embedded scalable speech and audio codec providing high quality narrowband speech over the lower bit rates and high quality wideband speech over the complete range of bit rates. In addition, G.718 is designed to be highly robust to frame erasures, thereby enhancing the speech quality when used in Internet Protocol (IP) transport applications on fixed, wireless and mobile networks. Despite its embedded nature, the codec also performs well with both narrowband and wideband generic audio signals. The codec has an embedded scalable structure, enabling maximum flexibility in the transport of voice packets through IP networks of today and in future media-aware networks. In addition, the embedded structure of G.718 will easily allow the codec to be extended to provide a superwideband and stereo capability through additional layers which are currently under development in ITU-T Study Group 16. The bitstream may be truncated at the decoder side or by any component of the communication system to instantaneously adjust the bit rate to the desired value without the need for out-of-band signalling. The encoder produces an embedded bitstream structured in five layers corresponding to the five available bit rates: 8, 12, 16, 24 & 32 kbit/s.
In information theory, a soft-decision decoder is a kind of decoding methods – a class of algorithm used to decode data that has been encoded with an error correcting code. Whereas a hard-decision decoder operates on data that take on a fixed set of possible values, the inputs to a soft-decision decoder may take on a whole range of values in-between. This extra information indicates the reliability of each input data point, and is used to form better estimates of the original data. Therefore, a soft-decision decoder will typically perform better in the presence of corrupted data than its hard-decision counterpart.
A locally decodable code (LDC) is an error-correcting code that allows a single bit of the original message to be decoded with high probability by only examining a small number of bits of a possibly corrupted codeword. This property could be useful, say, in a context where information is being transmitted over a noisy channel, and only a small subset of the data is required at a particular time and there is no need to decode the entire message at once. Note that locally decodable codes are not a subset of locally testable codes, though there is some overlap between the two.
