Errorcorrection

Error correction refers to methods used to detect and repair errors that occur during data transmission or storage. It encompasses both error detection—identifying that corruption has happened—and error correction—recovering the original data without the need for retransmission. Redundancy is introduced into the data to reveal and fix errors.

Common error-detection techniques include parity bits, checksums, and cyclic redundancy checks (CRC). Error-correcting codes add structured redundancy that enables recovery of the original information after corruption. Classic examples include Hamming codes, which can correct single-bit errors and detect certain multi-bit errors, and Reed-Solomon codes, which are widely used in CDs, DVDs, QR codes, and data transmission. More advanced schemes include convolutional and block codes, as well as modern low-density parity-check (LDPC) codes and turbo codes used in high-rate communications.

Theoretical foundations come from coding theory, which studies how to maximize reliable information transfer under noise constraints. The Shannon limit describes the theoretical maximum information rate that can be transmitted over a noisy channel with arbitrarily low error probability. Practical decoding uses algorithms such as maximum likelihood decoding, belief propagation, and iterative decoding to estimate the most probable original data given the received signal and the code structure.

Applications span digital communications, data storage, and information integrity. Error correction underpins Wi-Fi and cellular networks, satellite links, CDs, DVDs, and hard drives and solid-state drives. It also supports data reliability in QR codes, barcodes, and fault-tolerant computing and distributed storage systems that require redundancy to tolerate failures.