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Reed-Solomon codes are algebraic codes for forward error correction. Reed-Solomon codes have wide range of applications in digital communication and storage, such as CDs, DVDs, DVB and WiMAX.
A Reed-Solomon encoder takes digital data blocks and adds extra redundant bits. The Reed-Solomon decoder processes every block and attempts to correct errors and recover the original data where the number and type of errors to be corrected is based on the Reed-Solomon code characteristic. These codes achieve the largest code minimum distance for linear codes with the same encoder inputs and output block lengths. The distance between two code words for nonbinary codes is defined as the number of symbols in which sequences differ.
Reed-Solomon codes were invented by Irving S. Reed and Gustave Solomonin 1960, and continue to have a wide range of applications in digital communication and storage.
Algebraic decoding can correct errors and erasures. The probability of an error remaining in decoded data is always lower than the probability of an error if Reed-Solomon is not used.
Reed-Solomon encoding and decoding can be performed in software or special-purpose hardware. These codes are based on Galois fields, where arithmetic operations on field elements have a result in the field. An encoder or decoder handles these arithmetic operations, which require special software or hardware functions.