Coding for high-density recording on a 1-D granular magnetic medium

Arya Mazumdar, Alexander Barg, Navin Kashyap

Research output: Contribution to journalArticle

23 Scopus citations


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.

Original languageEnglish (US)
Article number5934413
Pages (from-to)7403-7417
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 1 2011

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