Chernoff boundIn probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian). It is especially useful for sums of independent random variables, such as sums of Bernoulli random variables. The bound is commonly named after Herman Chernoff who described the method in a 1952 paper, though Chernoff himself attributed it to Herman Rubin.
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 .
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.
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.
Musical formIn music, form refers to the structure of a musical composition or performance. In his book, Worlds of Music, Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a piece of music, such as "the arrangement of musical units of rhythm, melody, and/or harmony that show repetition or variation, the arrangement of the instruments (as in the order of solos in a jazz or bluegrass performance), or the way a symphonic piece is orchestrated", among other factors.
Interest rateAn interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized.
Video codecA video codec is software or hardware that compresses and decompresses digital video. In the context of video compression, codec is a portmanteau of encoder and decoder, while a device that only compresses is typically called an encoder, and one that only decompresses is a decoder. The compressed data format usually conforms to a standard video coding format. The compression is typically lossy, meaning that the compressed video lacks some information present in the original video.
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.
Sonata formSonata form (also sonata-allegro form or first movement form) is a musical structure generally consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle of the 18th century (the early Classical period). While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement.
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.
Binary formBinary form is a musical form in 2 related sections, both of which are usually repeated. Binary is also a structure used to choreograph dance. In music this is usually performed as A-A-B-B. Binary form was popular during the Baroque period, often used to structure movements of keyboard sonatas. It was also used for short, one-movement works. Around the middle of the 18th century, the form largely fell from use as the principal design of entire movements as sonata form and organic development gained prominence.
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.
Communication channelA 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.
Bit rateIn telecommunications and computing, bit rate (bitrate or as a variable R) is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction with an SI prefix such as kilo (1 kbit/s = 1,000 bit/s), mega (1 Mbit/s = 1,000 kbit/s), giga (1 Gbit/s = 1,000 Mbit/s) or tera (1 Tbit/s = 1,000 Gbit/s). The non-standard abbreviation bps is often used to replace the standard symbol bit/s, so that, for example, 1 Mbps is used to mean one million bits per second.
StandardizationStandardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments. Standardization can help maximize compatibility, interoperability, safety, repeatability, or quality. It can also facilitate a normalization of formerly custom processes.
Hamming boundIn mathematics and computer science, in the field of coding theory, the Hamming bound is a limit on the parameters of an arbitrary block code: it is also known as the sphere-packing bound or the volume bound from an interpretation in terms of packing balls in the Hamming metric into the space of all possible words. It gives an important limitation on the efficiency with which any error-correcting code can utilize the space in which its code words are embedded. A code that attains the Hamming bound is said to be a perfect code.
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Birth rateBirth rate, also known as natality, is the total number of live human births per 1,000 population for a given period divided by the length of the period in years. The number of live births is normally taken from a universal registration system for births; population counts from a census, and estimation through specialized demographic techniques. The birth rate (along with mortality and migration rates) is used to calculate population growth. The estimated average population may be taken as the mid-year population.
