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Abstract
As higher and higher densities are demanded in digital magnetic storage systems, communication theory plays an increasing role in the design of the systems. We present two applications of information theory and one application of error correction coding to magnetic hard drives. The first application of information theory is a new algorithm (called the bit stuff algorithm) for run-length-limiting and charge constraining binary data. This algorithm is both simple and universal. We show it to be optimal for the ($d,\infty,\infty$), the ($d,d+1,\infty$), and the ($2c-2,\infty,c$) constraints and nearly optimal for all other ($d,k,c$) constraints. The second application of information theory is a new universal data compression algorithm (called the improved Lempel-Ziv algorithm) for performing information lossless, on-line, data compression. We prove that the compression achieved by an individual codeword generated by either the original or the improved Lempel-Ziv algorithms asymptotically approaches the entropy of the data with probability one. In addition, we prove that the new algorithm will never do worse and will likely do better than the original Lempel-Ziv algorithm. Next, we show the new algorithm out-performs other data compression algorithms under the constraints imposed by a disk drive. Finally, we show how to incorporate the new algorithm into a magnetic disk drive. The application of error correction coding experimentally shows the performance increases when powerful Reed-Solomon error correction codes are used with a magnetic disk drive. Using AHA4010 Reed-Solomon encoder/decoder integrated circuits and Xilinx 3042 field programmable gate arrays, we designed and built a circuit for performing powerful Reed-Solomon error correction on a magnetic disk drive. We used the circuit to make off-track error rate measurements using several different error correction capabilities and different linear densities. We showed that one could increase the user bit density by using increasing the linear bit density and using powerful error correction codes to compensate for the increased error rate.
