"The RAID system built into Linux uses Reed-Solomon. It has a carefully tuned Reed-Solomon implementation in C that is part of the RAID module. Microsoft Azure uses a similar, but different, erasure coding strategy. We’re not sure exactly what Amazon S3 and Google Cloud Storage use because they haven’t said, but it’s bound to be Reed-Solomon or something similar. Facebook’s new cold storage system also uses Reed-Solomon."
https://www.backblaze.com/blog/reed-solomon/
"CDs can recover from scratches that corrupt up to 4000 bits thanks to the clever use of two Reed-Solomon codes."
CDs Recover from Scratches with Reed-Solomon Codes
Compact discs (CDs) can recover from scratches that corrupt up to 4000 bits thanks to the use of a sophisticated error correction scheme known as Cross-Interleaved Reed–Solomon Coding (CIRC).
- This system employs two concatenated Reed–Solomon codes, which are interleaved cross-wise to combat both random and burst errors effectively.
- The first, an inner (32,28) Reed–Solomon code, can correct up to 2 byte errors per 32-byte block and flags any uncorrectable blocks as erasures.
- These erasures are then processed by a deinterleaver, which spreads the information across multiple blocks of a second, outer (28,24) Reed–Solomon code.
- This outer code can correct up to 4 erasures per block, allowing the system to completely correct error bursts up to 4000 bits in sequence, equivalent to approximately 2.5 mm on the disc surface.
- This robust error correction capability ensures that most playback issues are due to tracking errors rather than uncorrectable data corruption.
https://tomverbeure.github.io/2022/08/07/Reed-Solomon.html
"In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.[1] They have many applications, including consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, Data Matrix, data transmission technologies such as DSL and WiMAX, broadcast systems such as satellite communications, DVB and ATSC, and storage systems such as RAID 6.
Reed–Solomon codes operate on a block of data treated as a set of finite-field elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding t = n − k check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to t erroneous symbols, or locate and correct up to ⌊t/2⌋ erroneous symbols at unknown locations.
As an erasure code, it can correct up to t erasures at locations that are known and provided to the algorithm, or it can detect and correct combinations of errors and erasures. Reed–Solomon codes are also suitable as multiple-burst bit-error correcting codes, since a sequence of b + 1 consecutive bit errors can affect at most two symbols of size b. The choice of t is up to the designer of the code and may be selected within wide limits. There are two basic types of Reed–Solomon codes – original view and BCH view – with BCH view being the most common, as BCH view decoders are faster and require less working storage than original view decoders."
https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_correction
"Backblaze B2 runs with 17 + 3, allowing it to tolerate 3 failures using 1.18x the storage space. OVH Cloud uses an 8 + 4 code, allowing it to tolerate 4 failures using 1.5x the storage space. Scaleway uses a 6 + 3 code, tolerating three failures using 1.5x the storage space."
https://transactional.blog/blog/2024-erasure-coding
https://berthub.eu/articles/posts/reed-solomon-for-programmers/
https://www.cs.cmu.edu/~guyb/realworld/reedsolomon/reed_solomon_codes.html
https://ntrs.nasa.gov/api/citations/19900019023/downloads/19900019023.pdf
https://blog.min.io/erasure-coding/
https://www.backblaze.com/docs/cloud-storage-resiliency-durability-and-availability
https://github.com/klauspost/reedsolomon