Correcting grain-errors in magnetic media

This paper studies new bounds and constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. The main theme of the paper is that codes capable of correcting grain-errors are related to codes that correct insertions/deletions and codes that correct asymmetric errors. Using this insight, new bounds on the maximum cardinality of a grain-error correcting code are derived and constructions of codes that correct grain-errors are considered. It is also demonstrated that permutations of the classical group codes can correct a single grain-error. In several cases of interest, our results improve upon the currently best known bounds and constructions.