Multiple error detecting and correcting system employing reed-solomon

Abstract

An error detecting and correcting system implementing the Reed-Solomon (1023, 1006) code having code words whose symbols are elements in the Galois field GF(2.sup.10) generated by either the primitive polynomial x.sup.10 +x.sup.3 +1 or x.sup.10 +x.sup.7 +1. An original data word is encoded to produce a code word w(x) including a first set of checksum symbols appended thereto. Upon retrieval, the data symbols of the receive code word y(x) are encoded by the same encoder that encodes the original data word to produce a second set of checksum symbols. Both sets of checksum symbols are modulo-two summed to produce a residue R(x) from which error syndromes S.sub.i can be computed and thus enable rapid correction of errors in the received code word y(x). The system also monitors the number of non-zero symbols in the residue R(x) in order to avoid unnecessary computation of error syndromes S.sub.i and other decoding routines, such as when the received code word y(x) is otherwise uncorrectable or when the error exists only in the received checksum symbols, rather than in the data symbols. The distance between code words being (2T+ 2), the error correction routine is bypassed when the number of non-zero symbols in R(x) is less than or equal to T, which indicates that errors only reside in the checksum symbols. When the number of non-zero symbols equals (T+1), the error is uncorrectable. For determining whether a single error exists so that correction can quickly be made, the system also tests whether S.sub.i+1 /S.sub.i is constant for all error syndromes S.sub.i.