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| Error detection and correction | |
|---|---|
| Name | Error detection and correction |
| Field | Information theory, Computer science, Electrical engineering |
| Invented | 1940s–1950s |
| Developers | Claude Shannon, Richard Hamming, Irving Reed, Gustave Solomon |
Error detection and correction Error detection and correction comprises methods and systems developed to identify and remedy errors arising in data storage, transmission, and processing. It spans theoretical foundations in Claude Shannon's information theory, practical algorithms by Richard Hamming and Irving S. Reed, and implementations across technologies pioneered by organizations such as AT&T, Bell Labs, and IBM. Applications range from deep-space missions of NASA to consumer electronics from Sony and Samsung, and from networking led by Cisco Systems to satellite communications by SpaceX.
Error detection and correction emerged during the mid-20th century with foundational work at Bell Labs and in wartime and postwar engineering projects such as ENIAC and efforts at Los Alamos National Laboratory. Key figures include Claude Shannon, Richard Hamming, Irving S. Reed, and Gustave Solomon, who formalized concepts that underpin modern coding theory used by AT&T, IBM, Intel, Microsoft, and Google. Standards bodies like the IEEE and IETF have codified techniques into protocols adopted by AT&T, Verizon Communications, Deutsche Telekom, and telecommunications firms in Japan such as NTT. The field links to mathematics developments at institutions like Princeton University and Massachusetts Institute of Technology.
Errors arise from physical and logical causes in systems built by corporations such as Intel Corporation and AMD. In storage media (e.g., drives by Western Digital and Seagate Technology), errors stem from wear, as studied in research at Stanford University and University of California, Berkeley. In wireless channels used by Qualcomm and Nokia, multipath fading, interference researched at Bell Labs and ETH Zurich, and Doppler shifts encountered by NASA missions produce bit flips. Cosmic-ray induced soft errors first noted in aerospace projects and investigated at Los Alamos National Laboratory and Jet Propulsion Laboratory affect electronics in Lockheed Martin and Boeing platforms. Human errors in deployments at Facebook and Twitter can introduce logical faults.
Detection methods include parity schemes used in systems from IBM mainframes, checksums adopted in protocols by IETF and Internet Engineering Task Force members, and cryptographic hashes implemented by RSA Security and NIST standards. Cyclic redundancy checks (CRC) standardized by ETSI and used in Ethernet specifications from Xerox and DEC provide robust frame error detection. Sequence-number and acknowledgment mechanisms originally employed in ARPANET and formalized in protocols by Vint Cerf and Bob Kahn (associated with DARPA) assist detection in transport protocols used by Cisco Systems. Hardware parity bits appear in memory modules by Kingston Technology and Corsair.
Correction techniques vary from simple retransmission strategies seen in TCP implementations used by Microsoft and Google to forward error correction (FEC) schemes such as Hamming codes, Reed–Solomon codes invented by Irving S. Reed and Gustave Solomon, and convolutional codes applied in products by Qualcomm and Ericsson. Turbo codes and LDPC codes, advanced by researchers at Thales Group and European Space Agency collaborations, enable high-throughput correction in cellular systems by Nokia and satellite modems by Hughes Network Systems. Hybrid ARQ, used in 3G/4G systems developed by Ericsson and Huawei, combines retransmission with FEC for improved reliability.
Foundations rest on concepts introduced by Claude Shannon and formalized within algebraic structures studied at University of Cambridge and Harvard University. Algebraic coding theory uses finite fields built on work by Évariste Galois and combinatorics advanced at Princeton University. Linear codes, cyclic codes, and polynomial representations draw on mathematics from Cambridge University Press curricula and derive algorithms implemented in libraries by GNU projects and research at MIT. Decoding algorithms—such as Viterbi, based on work by Andrew Viterbi, and belief propagation used in LDPC—are applied in systems by Qualcomm, Intel, and in standards by 3GPP.
Implemented in devices from Apple Inc. and Samsung Electronics to enterprise systems from Oracle Corporation and EMC Corporation, error control is integral to solid-state drives, mobile networks, satellite links, and broadcast television by BBC and NHK. Space missions by NASA and ESA rely on Reed–Solomon and convolutional schemes; deep-space probes from Jet Propulsion Laboratory used by NASA demonstrate long-delay FEC strategies. Optical communications in equipment by Corning Incorporated and submarine cable systems operated by TE SubCom use error control to maintain throughput. Standards organizations such as IEEE Standards Association and ITU specify coding in wired and wireless systems adopted by vendors like Cisco Systems, Ericsson, and Huawei.
Performance metrics include bit error rate (BER), frame error rate (FER), latency measured in standards by ITU-T, and throughput clauses in protocols from IETF. Trade-offs weigh redundancy overhead in storage products from Seagate Technology and Western Digital against decoding complexity implemented in silicon by Intel and ARM Holdings, and energy consumption in mobile chipsets by Qualcomm and MediaTek. Regulatory frameworks influenced by agencies such as Federal Communications Commission and European Commission affect spectrum use and resilience requirements for telecom providers like Vodafone and T-Mobile International.