Cyclic code decoding method and cyclic code decoder

A cyclic code decoding method having an error correcting capability for correcting a maximum number of correctable errors in a received codeword that has a plurality of symbols, said cyclic code decoding method to be implemented using a cyclic code decoder that includes a syndrome calculator, an error location polynomial generator, and an error correction device, and comprising the following steps of:

• a) configuring the cyclic code decoder to analyze the received codeword so as to identify unreliable ones of the symbols;
• b) configuring the cyclic code decoder to set a group of candidate syndrome patterns according to the unreliable ones of the symbols;
• c) configuring the syndrome calculator to calculate a number of evaluated syndrome values according to the received codeword and one of the candidate syndrome patterns, the number of the evaluated syndrome values being twice the maximum number of the correctable errors;
• d) configuring the error location polynomial generator to generate, according to the evaluated syndrome values, an error location polynomial with a degree not more than the maximum number of the correctable errors;
• e) configuring the error location polynomial generator to determine whether the degree of the error location polynomial is greater than a threshold value, which is less than the maximum number of the correctable errors;
• f) when it is determined in step e) that the degree of the error location polynomial is greater than the threshold value, configuring the syndrome calculator to adjust the evaluated syndrome values so as to be associated with another one of the candidate syndrome patterns, and configuring the error location polynomial generator to repeat steps d) and e) with the evaluated syndrome values thus adjusted;
• and
• g) when it is determined in step e) that the degree of the error location polynomial is not greater than the threshold value, configuring the error correction device to correct the correctable errors in the received codeword according to a root of the error location polynomial.