Arabic scriptThe Arabic script is the writing system used for Arabic and several other languages of Asia and Africa. It is the second-most widely used alphabetic writing system in the world (after the Latin alphabet), the second-most widely used writing system in the world by number of countries using it or a script directly derived from it, and the third-most by number of users (after the Latin and Chinese scripts). The script was first used to write texts in Arabic, most notably the Quran, the holy book of Islam.
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.
Universal code (data compression)In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., p(i) ≥ p(i + 1) for all positive i), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned.
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.
ThetaTheta (UKˈθiːtə, USˈθeɪtə; uppercase: Θ or ; lowercase: θ or ; thē̂ta thɛ̂ːta; Modern: thī́ta ˈθita) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals, it has a value of 9. In Ancient Greek, θ represented the aspirated voiceless dental plosive t̪h, but in Modern Greek it represents the voiceless dental fricative θ. In its archaic form, θ was written as a cross within a circle (as in the Etruscan or ), and later, as a line or point in circle ( or ).
Error exponentIn information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ratio of the negative logarithm of the error probability to the block length of the code for large block lengths. For example, if the probability of error of a decoder drops as , where is the block length, the error exponent is . In this example, approaches for large .
Best, worst and average caseIn computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n.
Entropy codingIn information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have expected code length greater or equal to the entropy of the source. More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies , where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol.
Cost of capitalIn economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet. For an investment to be worthwhile, the expected return on capital has to be higher than the cost of capital.
Prior probabilityA prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.
