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.
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.
Viterbi decoderA Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice. Viterbi decoding was developed by Andrew J.
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.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
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.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
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.
Time-sharingIn computing, time-sharing is the sharing of a computing resource among many users at the same time by means of multiprogramming and multi-tasking. Its emergence as the prominent model of computing in the 1970s represented a major technological shift in the history of computing. By allowing many users to interact concurrently with a single computer, time-sharing dramatically lowered the cost of providing computing capability, made it possible for individuals and organizations to use a computer without owning one, and promoted the interactive use of computers and the development of new interactive applications.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Iterative and incremental developmentIterative and incremental development is any combination of both iterative design or iterative method and incremental build model for development. Usage of the term began in software development, with a long-standing combination of the two terms iterative and incremental having been widely suggested for large development efforts. For example, the 1985 DOD-STD-2167 mentions (in section 4.1.2): "During software development, more than one iteration of the software development cycle may be in progress at the same time.
Shannon's source coding theoremIn information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that (in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity) it is impossible to compress the data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost.
Neuronal ensembleA neuronal ensemble is a population of nervous system cells (or cultured neurons) involved in a particular neural computation. The concept of neuronal ensemble dates back to the work of Charles Sherrington who described the functioning of the CNS as the system of reflex arcs, each composed of interconnected excitatory and inhibitory neurons. In Sherrington's scheme, α-motoneurons are the final common path of a number of neural circuits of different complexity: motoneurons integrate a large number of inputs and send their final output to muscles.
Unilineal evolutionUnilineal evolution, also referred to as classical social evolution, is a 19th-century social theory about the evolution of societies and cultures. It was composed of many competing theories by various anthropologists and sociologists, who believed that Western culture is the contemporary pinnacle of social evolution. Different social status is aligned in a single line that moves from most primitive to most civilized. This theory is now generally considered obsolete in academic circles.
Student's t-distributionIn probability and statistics, Student's t-distribution (or simply the t-distribution) is a continuous probability distribution that generalizes the standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, has heavier tails and the amount of probability mass in the tails is controlled by the parameter . For the Student's t distribution becomes the standard Cauchy distribution, whereas for it becomes the standard normal distribution .
Newton's methodIn numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then is a better approximation of the root than x0.
Neural codingNeural coding (or neural representation) is a neuroscience field concerned with characterising the hypothetical relationship between the stimulus and the individual or ensemble neuronal responses and the relationship among the electrical activity of the neurons in the ensemble. Based on the theory that sensory and other information is represented in the brain by networks of neurons, it is thought that neurons can encode both digital and analog information.
Photocatalytic water splittingPhotocatalytic water splitting is a process that uses photocatalysis for the dissociation of water (H2O) into hydrogen (H2) and oxygen (O2). Only light energy (photons), water, and a catalyst(s) are needed, since this is what naturally occurs in natural photosynthetic oxygen production and CO2 fixation. Photocatalytic water splitting is done by dispersing photocatalyst particles in water or depositing them on a substrate, unlike Photoelectrochemical cell, which are assembled into a cell with a photoelectrode.
