A communication channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking. A channel is used for information transfer of, for example, a digital bit stream, from one or several senders to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second.
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.
In 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 .
Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.
In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters. In the algebra of random variables, inverse distributions are special cases of the class of ratio distributions, in which the numerator random variable has a degenerate distribution.
In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: where pi is the probability of the system being in state i, exp is the exponential function, εi is the energy of that state, and a constant kT of the distribution is the product of the Boltzmann constant k and thermodynamic temperature T.
A 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.
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. C. Mahalanobis in 1936. Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls based on measurements in 1927. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. This distance is zero for P at the mean of D and grows as P moves away from the mean along each principal component axis.
In 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 .
