Fast decoder and encoder for reed-solomon codes

Details Fast decoder and encoder for reed-solomon codes Fast decoder and encoder for reed-solomon codes

H - Electricity

03

M

354/67

H03M 13/00 (2006.01) G06F 7/72 (2006.01) G11B 20/18 (2006.01) H03M 13/15 (2006.01)

Patent

CA 1229169

31 ABSTRACT: A decoding device for code words which are pro- tected against the occurrence of several symbol errors per code word by means of a Reed-Solomon code is provided with a word buffer which comprises a space for the storage of an erasure indication per symbol received. For correction of the code word, first the syndrome symbols are formed by multiplication by the parity check matrix. The sum of twice the number of error symbols and once the number of erasure symbols may not be larger than the number of syn- drome symbols. First the syndrome symbols are modified so that the syndrome symbols which could possibly relate to error symbols (non-erasure symbols) are no longer influ- enced by the erasure symbols. The key equation and error locator equation for the non-influenced syndrome symbols can then be separately solved, so that the locations of error symbols can be found. The latter syndrome symbols are then modified, when necessary, for calculated error locations, while the error values or erasure values are determined from a set of mutually independent syndrome symbols whose number equals the sum of error symbols and erasure symbols. There is provided an arithmetic unit for the Galois-field which, for the sake of simplicity, per- forms the calculations on the exponents of the symbols which are written as powers of the basic symbol of the Galois-field.

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