Correcting Grain-Errors in Magnetic Media
This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models.
© 2015 IEEE. Manuscript received July 25, 2013; revised December 1, 2014; accepted January 5, 2015. Date of publication March 4, 2015; date of current version April 17, 2015. This work was supported in part by the Division of Computing and Communication Foundations through the NSF under Grant CCF-1029030 and Grant CCF-1150212, in part by the ISEF Foundation, and in part by the SMART Scholarship. This paper was presented in part at the 2013 IEEE International Symposium on Information Theory. The authors would like to thank Artyom Sharov for his helpful discussions about code cardinalities as well as Associate Editor Prof. Navin Kashyap and the anonymous reviewers for providing detailed and expert comments.
Submitted - 1307.7087v1.pdf