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.
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.
Algebraic structureIn mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures.
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.
Hamming(7,4)In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correcting codes.
System of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple since it makes all three equations valid. The word "system" indicates that the equations should be considered collectively, rather than individually.
CodebookA codebook is a type of document used for gathering and storing cryptography codes. Originally codebooks were often literally books, but today codebook is a byword for the complete record of a series of codes, regardless of physical format. In cryptography, a codebook is a document used for implementing a code. A codebook contains a lookup table for coding and decoding; each word or phrase has one or more strings which replace it. To decipher messages written in code, corresponding copies of the codebook must be available at either end.
JPEGJPEG (ˈdʒeɪpɛɡ , short for Joint Photographic Experts Group) is a commonly used method of lossy compression for s, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable tradeoff between storage size and . JPEG typically achieves 10:1 compression with little perceptible loss in image quality. Since its introduction in 1992, JPEG has been the most widely used standard in the world, and the most widely used digital , with several billion JPEG images produced every day as of 2015.
Linear regressionIn statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
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 .
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.
Systematic codeIn coding theory, a systematic code is any error-correcting code in which the input data is embedded in the encoded output. Conversely, in a non-systematic code the output does not contain the input symbols. Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do not need to recover the original source symbols if received correctly – this is useful for example if error-correction coding is combined with a hash function for quickly determining the correctness of the received source symbols, or in cases where errors occur in erasures and a received symbol is thus always correct.
