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Reed–Solomon codes are an important group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960. They have many important applications, the most prominent of which include consumer technologies such as CDs, DVDs, Blu-ray Discs, QR Codes, data transmission technologies such as DSL and WiMAX, broadcast systems such as DVB and ATSC, and storage systems such as RAID 6. They are also used in satellite communication. In coding theory, the Reed–Solomon code belongs to the class of non-binary cyclic error-correcting codes. The Reed–Solomon code is based on univariate polynomials over finite fields. It is able to detect and correct multiple symbol errors. By adding check symbols to the data, a Reed–Solomon code can detect any combination of up to erroneous symbols, or correct up to symbols. As an erasure code, it can correct up to known erasures, or it can detect and correct combinations of errors and erasures. Furthermore, Reed–Solomon codes are suitable as multiple-burst bit-error correcting codes, since a sequence of consecutive bit errors can affect at most two symbols of size . The choice of is up to the designer of the code, and may be selected within wide limits. ==History== Reed–Solomon codes were developed in 1960 by Irving S. Reed and Gustave Solomon, who were then staff members of MIT Lincoln Laboratory. Their seminal article was titled "Polynomial Codes over Certain Finite Fields.". When the article was written, an efficient decoding algorithm was not known. A solution for the latter was found in 1969 by Elwyn Berlekamp and James Massey, and is since known as the Berlekamp–Massey decoding algorithm. In 1977, Reed–Solomon codes were notably implemented in the Voyager program in the form of concatenated error correction codes. The first commercial application in mass-produced consumer products appeared in 1982 with the compact disc, where two interleaved Reed–Solomon codes are used. Today, Reed–Solomon codes are widely implemented in digital storage devices and digital communication standards, though they are being slowly replaced by more modern low-density parity-check (LDPC) codes or turbo codes. For example, Reed–Solomon codes are used in the Digital Video Broadcasting (DVB) standard DVB-S, but LDPC codes are used in its successor, DVB-S2. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Reed–Solomon error correction」の詳細全文を読む スポンサード リンク
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