Artyom Sharov – Bounds and constructions for granular media coding

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The essential building blocks of conventional magnetic recording media are so-called grains
which are two-dimensional arbitrarily-shaped magnetizable units assuming one of two possible types of polarity. In modern technologies, the writing medium is partitioned into cells, typically larger in size than the grains, thereby determining how the process of setting a value to a cell is carried out, namely, the process boils down to magnetizing all the grains within the boundaries of this cell. Recently, a novel mechanism was proposed by Wood et al. that enables to magnetize areas that are proportionate in their size to the size of grains effectively creating a different type of medium where the grain polarity is determined by the last bit written into the grain. Recording with areal densities this high introduces errors to the neighboring cells of the cell being written (“grain errors”) and motivates the construction of codes which are capable of correcting those grain errors (“grain-correcting codes”).

In this talk, we will define a new combinatorial error model describing grain errors and present lower and upper bounds on the rates of grain-correcting codes. If time permits, we will show constructions of grain-correcting codes of length n correcting t errors for certain values of n and t and mention grain-detecting codes as well.