Error correction decoder, error correction value generator, and error correction system

An error correction value generator adapted for use in an error correction decoder that is coupled to an error correcting device for providing the error correcting device with an error correction value to correct an error corresponding to an error position of a received signal received by the error correction decoder, and that includes a syndrome generator operable to generate a plurality of syndromes based upon the received signal, each of the syndromes being associated with a respective index, the received signal being generated based upon a generator polynomial,

• said error correction value generator being adapted to be coupled to the syndrome generator for receiving the syndromes therefrom, and comprising:
• a first computing module operable to generate a plurality of product values, each of which is generated for one of the syndromes based upon a respective power of roots of the generator polynomial, the respective power being determined based upon the respective index corresponding to one of the syndromes to be considered and unit positions of the received signal;
• and
• a second computing module coupled to said first computing module, said second computing module being operable to generate the error correction value according to the product values obtained by said first computing module, and to provide the error correcting device with the error correction value computed thereby for correcting the error of the received signal.

An error correction system adapted for correcting an error corresponding to an error position of a received signal received thereby, the received signal being generated based upon a generator polynomial, said error correction system comprising:

• an error correction decoder including
• a syndrome generator adapted to receive the received signal, and operable to generate a plurality of syndromes based upon the received signal, each of the syndromes being associated with a respective index, and
• an error correction value generator coupled to said syndrome generator and being operable to generate a plurality of error correction values according to the syndromes received from said syndrome generator;
• and
• an error correcting device coupled to said error correction value generator and adapted to receive the error correction values therefrom, said error correcting device being operable to correct the error of the received signal according to the error correction values;
• wherein said error correction value generator of said error correction decoder includes
• a first computing module being operable to generate a group of product values for each of unit positions of the received signal, each of the product values of the same group being generated based upon one of the syndromes and a respective power of roots of the generator polynomial, the respective power being determined based upon the respective index corresponding to one of the syndromes to be considered and the corresponding one of the unit positions, and
• a second computing module coupled to said first computing module, and being operable to generate the error correction values according to the groups of the product values, respectively.