The Taub Faculty of Computer Science Events and Talks

Conventional magnetic recording media are composed of basic magnetizable two-dimensional units called grains, which might be random in size and shape. Recently, a new technological enhancement was proposed, which enables magnetizing areas as small as the size of grains. This novelty effectively created a different type of medium, in which one observes a new type of errors. Handling such errors is the main subject of this work. We first consider a combinatorial model of this medium, where so-called grain-correcting codes are used to handle worst-case error patterns. We also study a variant of this model where the errors are allowed to overlap (the supporting application of this variant can be found in shingled writing on bit-patterned media). For these two models, we present improved lower and upper bounds on the size and the growth rate of grain-correcting codes. In addition, we give explicit constructions of grain-correcting codes for correcting very small or very large number of errors. We then switch to the problem of detecting grain errors and provide lower and upper bounds on the minimum redundancy of codes that can detect any number of grain errors. Then, we turn to a probabilistic characterization of overlapping grain error patterns as a generalized Ising channel, for which we give almost-tight bounds on the capacity. We also consider a variant of this channel where feedback is added and compute lower bounds on its capacity. Moreover, for a certain range of values of the channel error probability, we establish a closed-form expression for that capacity.