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Coding for High-Density Recording on a 1-D Granular Magnetic Medium

Mazumdar, Arya and Barg, Alexander and Kashyap, Navin (2011) Coding for High-Density Recording on a 1-D Granular Magnetic Medium. In: IEEE Transactions on Information Theory, 57 (11). pp. 7403-7417.

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In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple 1-D combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.

Item Type: Journal Article
Publication: IEEE Transactions on Information Theory
Publisher: IEEE
Additional Information: Copyright 2011 IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 19 Dec 2011 12:00
Last Modified: 19 Dec 2011 12:00
URI: http://eprints.iisc.ac.in/id/eprint/42776

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