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

Author

Mita, Seiichi ; Matsui, Hajime

Author_Institution

Toyota Technol. Inst., Nagoya, Japan

Volume

41

Issue

10

fYear

2005

Firstpage

2992

Lastpage

2994

Abstract

This paper describes the performance of an efficient error-correcting system for hard disk drives. The performance of the codes on algebraic curves, such as Hermitian codes over GF(2⁸), elliptic codes over GF(2⁹), and Fermat codes over GF(2¹⁰) is compared with that of conventional Reed-Solomon (RS) codes. In particular, an adoption of Hermitian codes can reduce the redundant part by approximately 800 bits more than the RS codes when an error-correcting capability of 240 bytes is adopted for a long sector size. Moreover, we propose an error-correcting system based on a combination of algebraic geometric codes and parity codes. This combination system can cover a bit-error rate of approximately 10^-2 under a condition of EEPR4 channel and additive Gaussian noise.

Keywords

Reed-Solomon codes; algebraic geometric codes; error correction codes; error statistics; hard discs; parity check codes; Bahl-Cocke-Jelinek-Raviv algorithm; EEPR4 channel; Fermat codes; Hermitian codes; Reed-Solomon codes; additive Gaussian noise; algebraic curves; algebraic geometric codes; belief propagation algorithm; bit-error rate; elliptic codes; error correction; hard disk drives; magnetic recording channels; parity codes; Additive noise; Belief propagation; Bit error rate; Error correction codes; Gaussian noise; Hard disks; Helium; Magnetic noise; Magnetic recording; Preamplifiers; Algebraic geometric codes; Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm; Reed–Solomon (RS) codes; belief propagation algorithm; magnetic recording channels; parity codes;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2005.854451

Filename

1519184