| 摘要 |
An R-stage error correction system constructed in accordance with a distance d Reed-Soloman code performs a modified encoding step to include in the encoding a predetermined non-zero "coset symbol" that results in the encoder producing a code word for recording that includes a coset leader of a distance d-1 code. During the modified encoding step, the coset symbol is included in the value produced by the R<th>stage of the encoder during the encoding of a code word data symbol or a first redundancy symbol. The coset symbol is thereafter included in the encoding of the remaining redundancy symbols when the value produced by the last stage is fed back to the preceding stages. During decoding, the system decodes the code word and the included coset leader to generate associated error syndromes. In a last decoding step, the system removes the effects of the included coset leader from the syndromes, by combining a predetermined syndrome value with the syndrome value generated in the R<th>stage . If there is no synchronization error and the code word is error-free, the result is a set of all zero syndromes. If there are code word errors but no synchronization error, the system produces a non-zero syndrome pattern that is associated with a correctable number of errors. Otherwise, if there is a synchronization error, the inclusion of the predetermined syndrome value produces a syndrome pattern that is associated with an uncorrectable number of errors.
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