Coding theory

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Data scrubbing

Data scrubbing is an error correction technique that uses a background task to periodically inspect main memory or storage for errors, then corrects detected errors using redundant data in the form of different checksums or copies of data. Data scrubbing reduces the likelihood that single correctable errors will accumulate, leading to reduced risks of uncorrectable errors. Data integrity is a high-priority concern in writing, reading, storage, transmission, or processing of the computer data in computer operating systems and in computer storage and data transmission systems.

Code word

In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, clarity, brevity, or secrecy.

Entropy coding

In 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.

Data redundancy

In computer main memory, auxiliary storage and computer buses, data redundancy is the existence of data that is additional to the actual data and permits correction of errors in stored or transmitted data. The additional data can simply be a complete copy of the actual data (a type of repetition code), or only select pieces of data that allow detection of errors and reconstruction of lost or damaged data up to a certain level.

Generator matrix

In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix. If G is a matrix, it generates the codewords of a linear code C by where w is a codeword of the linear code C, and s is any input vector. Both w and s are assumed to be row vectors.

Binary erasure channel

In coding theory and information theory, a binary erasure channel (BEC) is a communications channel model. A transmitter sends a bit (a zero or a one), and the receiver either receives the bit correctly, or with some probability receives a message that the bit was not received ("erased") . A binary erasure channel with erasure probability is a channel with binary input, ternary output, and probability of erasure . That is, let be the transmitted random variable with alphabet .

Variable-length code

In coding theory, a variable-length code is a code which maps source symbols to a variable number of bits. The equivalent concept in computer science is bit string. Variable-length codes can allow sources to be compressed and decompressed with zero error (lossless data compression) and still be read back symbol by symbol. With the right coding strategy an independent and identically-distributed source may be compressed almost arbitrarily close to its entropy.

Systematic code

In 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.

Huffman coding

In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes". The output from Huffman's algorithm can be viewed as a variable-length code table for encoding a source symbol (such as a character in a file).

Channel capacity

Channel 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.