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.
Binary symmetric channelA binary symmetric channel (or BSCp) is a common communications channel model used in coding theory and information theory. In this model, a transmitter wishes to send a bit (a zero or a one), and the receiver will receive a bit. The bit will be "flipped" with a "crossover probability" of p, and otherwise is received correctly. This model can be applied to varied communication channels such as telephone lines or disk drive storage.
Root-finding algorithmsIn mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound).
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Criminal procedureCriminal procedure is the adjudication process of the criminal law. While criminal procedure differs dramatically by jurisdiction, the process generally begins with a formal criminal charge with the person on trial either being free on bail or incarcerated, and results in the conviction or acquittal of the defendant. Criminal procedure can be either in form of inquisitorial or adversarial criminal procedure.
Civil procedureCivil procedure is the body of law that sets out the rules and standards that courts follow when adjudicating civil lawsuits (as opposed to procedures in criminal law matters). These rules govern how a lawsuit or case may be commenced; what kind of service of process (if any) is required; the types of pleadings or statements of case, motions or applications, and orders allowed in civil cases; the timing and manner of depositions and discovery or disclosure; the conduct of trials; the process for judgment; the process for post-trial procedures; various available remedies; and how the courts and clerks must function.
Total variationIn mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure. For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x), for x ∈ [a, b]. Functions whose total variation is finite are called functions of bounded variation.
In-place algorithmIn computer science, an in-place algorithm is an algorithm that operates directly on the input data structure without requiring extra space proportional to the input size. In other words, it modifies the input in place, without creating a separate copy of the data structure. An algorithm which is not in-place is sometimes called not-in-place or out-of-place. In-place can have slightly different meanings. In its strictest form, the algorithm can only have a constant amount of extra space, counting everything including function calls and pointers.
Observational errorObservational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: random and systematic. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken.
