Error detection and correction

Error detection and correction comprises methods that identify errors in data and, when possible, restore the data to its intended form. These methods add or exploit redundancy to distinguish valid data from corrupted data.

Parity bit: A bit added to data so the total number of 1s is even or odd, enabling detection of some errors. A simple redundancy rule detects any odd number of bit flips in a block.
Data corruption: An unintended change to data that makes it differ from its intended or previously valid form. Detection and correction begin with distinguishing altered data from valid data.
Automatic repeat request: A communication protocol that detects failed or damaged transmissions and requests retransmission. It recovers data through repetition rather than correcting every error locally.
Error detection: The identification of corrupted data without necessarily determining its original value. Detection alone flags damage but cannot generally reconstruct the intended data.
Checksum: A value computed from data and stored or transmitted alongside it to help detect accidental changes. Checksums detect many corruptions without necessarily locating or correcting them.
Redundancy: The inclusion of more information than is strictly necessary to represent a message or perform a task. Extra information supplies the constraints that expose or repair errors.
Compact disc: An optical disc format that stores digital audio or data as pits and lands read by a laser. Interleaving and error-correcting codes help playback survive scratches and dust.
Error correction code: A code that adds structured redundancy so a decoder can detect or correct data errors. This formal coding framework encompasses many correction methods described here.
Cyclic redundancy check: An error-detecting code that represents bit strings as polynomials and computes a remainder using polynomial division. Its polynomial remainder detects common burst errors in communications and storage.
Hamming distance: The number of positions at which two equal-length strings differ. Codeword distances determine how many errors a code can detect or correct.

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