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.
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Manuscript received December 07, 2010; revised April 25, 2011; accepted May 24, 2011. Date of current version November 11, 2011. A. Mazumdar and A. Barg were supported by NSF Grants CCF0830699 and CCF0916919. N. Kashyap was supported in part by a Discovery Grant from NSERC, Canada, and performed this work while on sabbatical from Queen’s University, Kingston, ON, Canada, at the University of Maryland, College Park, and the Indian Institute of Science, Bangalore. This paper was presented in part at the 2010 IEEE International Symposium on Information Theory and in part at the 48th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, September 29–October 1, 2010.