Product Codes for Data Storage on Magnetic Tape

• Published in: IEEE transactions on magnetics Vol. 53; no. 2; pp. 1 - 10
• Main Authors: Cideciyan, Roy D., Furrer, Simeon, Lantz, Mark A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-02-2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Burst-error correction; Channel capacity; Coding; Computer simulation; Data storage; Decoding; Encoding; Error correction; Error correction codes; error-correction coding (ECC); Iterative decoding; Iterative methods; Magnetic tape; Magnetism; Materials management; Product codes; Three-dimensional displays; Two dimensional displays
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2016.2614010

For 2-D product codes used in tape storage, the mapping of error-correction-coding (ECC) blocks (EBs) into 2-D physical blocks (PBs) on magnetic tape is generalized. The 3-D product codes that have the same code rate and EB size as interleaved 2-D product codes currently used in tape storage are proposed. For 3-D product codes, a new family of mappings of EBs into 2-D PBs on magnetic tape is introduced, which fulfills the stringent burst-error-correction requirements of tape storage. The burst-error-correction capability of 2-D and 3-D product code words recorded on magnetic tape is analyzed as a function of track rotation, linear density, and ECC parameters. The performance limits of the tape-storage channel are determined based on computations of channel capacity and random coding bound. Hardware simulations of iterative hard-decision decoding of product codes implemented in a field-programmable gate array demonstrate the improved error-rate performance of 3-D product codes over 2-D product codes.