Codes Correcting Limited-Shift Errors in Racetrack Memories

In this work, we study limited-shift errors in racetrack memories and propose several schemes to combat these errors. There are two kinds of shift errors, namely under-shift errors, that can be modeled as sticky-insertions and limited-over-shift errors, that can be modeled as bursts of deletions of limited length. One approach to tackle the problem is to use deletion/sticky-insertion-correcting codes. Using this approach, we present a new family of asymptotically optimal codes that correct multiple bursts of deletions of limited length and any number of sticky insertions. We then study another approach that takes advantage of the special features of racetrack memories and the ability to add extra heads for redundancy. Here, we propose how to place the extra heads and construct codes to correct these shift errors.