An effective error correction using a combination of algebraic geometric codes and parity codes for HDD

The non-interleaving use of Reed-Solomon codes (RS codes) needs operations over GF(2 9) for current sector size (512 bytes) and operations over GF(2 12) for a long sector size (4096 bytes). However, main errors caused by media noise and thermal noise due to preamplifiers and magnetic heads are small size errors such as one bit or three consecutive bits. In order to correct these errors effectively, the performance of efficient error correcting codes on algebraic curves (algebraic geometric codes, AG codes) such as Hermitian code over GF(2 8), elliptic code over GF(2 9) and Fermat code over GF(2 10) with that of conventional RS codes was compared. Moreover, an error correcting system based on a combination of Hermitian codes and parity codes are proposed which takes advantage of redundant bits reduced by using AG codes.