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For two-dimensional (2D) product codes used in tape storage, the mapping of error-correction-coding (ECC) blocks into 2D physical blocks on magnetic tape is generalized. Three-dimensional (3D) product codes that have the same code rate and ECC block size as interleaved 2D product codes currently used in tape storage are proposed. For 3D product codes, a new family of mappings of ECC blocks into 2D physical blocks on magnetic tape is introduced, which fulfills the stringent burst-error-correction requirements of tape storage. The burst-error-correction capability of 2D and 3D product codewords 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 is 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 3D product codes over 2D product codes.
By: Roy D. Cideciyan, Simeon Furrer, Mark A. Lantz
Published in: IEEE Transactions on Magnetics, volume 53, (no 2), pages 10.1109/TMAG.2016.2614010 in 2016
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