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The 45 pages that link to Error-correcting code, each with the reason it gives.

• Signal-to-noise ratioRelated: Coding can make communication reliable even when the channel’s signal-to-noise ratio is limited.

• Information theoryBroader topic: Redundancy lets real systems approach reliable communication over noisy channels.

• CombinatoricsRelated: Combinatorial designs and distance bounds govern how many errors codes can withstand.

• Claude ShannonRelated: Shannon’s channel-coding theorem established the possibility of reliable communication using such codes.

• BitRelated: Redundant bit patterns allow corrupted data to be detected or corrected.

• Data compressionCompared with: It spends extra bits on reliability, whereas compression seeks to remove redundancy.

• OrthogonalityRelated: Orthogonal codewords can be distinguished reliably by inner-product measurements.

• Solid-state driveRelated: Flash controllers use error correction to recover data affected by cell errors.

• Hard disk driveRelated: The drive uses coded redundancy to recover data despite imperfect magnetic reads.

• Hamming distanceNarrower topic: Codewords are designed to remain far apart under Hamming distance.

• Analog signalCompared with: Digital communication can recover exact symbols in ways analog transmission generally cannot.

• Deep Space NetworkRelated: Coding protects information when deep-space signals arrive weak or corrupted.

• FieldRelated: Many practical codes perform their arithmetic over finite fields.

• DVDRelated: DVD error correction helps recover data despite scratches, dust, and read noise.

• NAND flash memoryRelated: NAND’s shrinking voltage margins make error correction necessary for reliable reads.

• Communication channelRelated: Redundancy helps recover messages corrupted while passing through the channel.

• LatticeRelated: Some codes use lattices to encode data and correct geometric noise.

• Shannon–Hartley theoremRelated: Codes approach the capacity limit by correcting noise-induced errors.

• Sphere packingNarrower topic: Sphere-packing arguments establish limits on code size and correction capability.

• USB flash driveRelated: Flash controllers use it to recover data affected by cell errors.

• Parity bitNarrower topic: Parity bits are a simple error-detection code, not a correction method.

• TelecommunicationsRelated: It protects transmitted information against noise and interference.

• A Mathematical Theory of CommunicationRelated: The channel coding theorem showed that redundancy can enable reliable transmission despite noise.

• Error detection and correctionBroader topic: This formal coding framework encompasses many correction methods described here.

• Blu-rayRelated: Blu-ray uses error correction to recover data despite scratches, dust, and read errors.

• ModemRelated: Modems use coding to recover data altered by noise during transmission.

• Magnetic-tape data storageRelated: Tape formats use redundancy to recover data affected by defects or read errors.

• Memory cardRelated: Controllers use error correction to recover data from imperfect flash cells.

• RAIDNarrower topic: RAID parity is one use of redundancy for recovering missing data.

• RedundancyBroader topic: These codes use deliberate redundancy to reconstruct data corrupted in transmission or storage.

• Hamming codeNarrower topic: Hamming codes are an early, compact construction within this broader family.

• SD cardRelated: Controllers use error correction to recover data affected by flash errors.

• Data storageRelated: Redundancy helps recover data when storage introduces errors.

• Cavity methodRelated: Cavity-inspired message passing estimates transmitted bits in sparse-graph codes.

• Flag semaphoreRelated: Repeated or confirmed semaphore signals help detect mistakes caused by distance or poor visibility.

• Gilbert–Varshamov boundNarrower topic: The bound describes how many codewords can exist at a given length and distance.

• Elwyn BerlekampRelated: Coding theory supplied the central problem behind much of Berlekamp’s engineering mathematics.

• Hamming boundNarrower topic: The Hamming bound limits the number of codewords such a set can contain.

• Mutually orthogonal Latin squaresRelated: Orthogonal arrays derived from squares support constructions of codes with controlled symbol balance.

• Reed–Solomon error correctionNarrower topic: Reed–Solomon correction is one specific form of error-correcting coding.

• Boole's inequalityRelated: Coding proofs use union bounds to control the chance that any competing codeword causes decoding failure.

• CD playerRelated: It lets playback recover audio despite small scratches and reading errors.

• Information and communication theoryBroader topic: These codes turn the theoretical promise of reliable transmission into explicit symbol patterns.

• Noisy-channel coding theoremRelated: Codes provide the redundancy that makes the theorem’s low-error transmission possible.

• PCP theoremRelated: Redundant encodings help make false proofs detectable through a few local queries.