Parity bitA parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), although they can also be applied separately to an entire message string of bits. The parity bit ensures that the total number of 1-bits in the string is even or odd. Accordingly, there are two variants of parity bits: even parity bit and odd parity bit.
Exponential distributionIn probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Bandwidth (computing)In computing, bandwidth is the maximum rate of data transfer across a given path. Bandwidth may be characterized as network bandwidth, data bandwidth, or digital bandwidth. This definition of bandwidth is in contrast to the field of signal processing, wireless communications, modem data transmission, digital communications, and electronics, in which bandwidth is used to refer to analog signal bandwidth measured in hertz, meaning the frequency range between lowest and highest attainable frequency while meeting a well-defined impairment level in signal power.
Gamma distributionIn probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter and a scale parameter . With a shape parameter and an inverse scale parameter , called a rate parameter. In each of these forms, both parameters are positive real numbers.
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.
Phase-type distributionA phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.
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.
Log-normal distributionIn probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
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 .
Repetition codeIn coding theory, the repetition code is one of the most basic linear error-correcting codes. In order to transmit a message over a noisy channel that may corrupt the transmission in a few places, the idea of the repetition code is to just repeat the message several times. The hope is that the channel corrupts only a minority of these repetitions. This way the receiver will notice that a transmission error occurred since the received data stream is not the repetition of a single message, and moreover, the receiver can recover the original message by looking at the received message in the data stream that occurs most often.
