Artyom Sharov, Ph.D. Thesis Seminar
Wednesday, 29.4.2015, 16:30
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.