Correcting Deletions in Multiple-Heads Racetrack Memories

Abstract

One of the main challenges in developing racetrack memory systems is the limited precision in controlling the track shifts, that in turn affects the reliability of reading and writing the data. The current proposal for combating deletions in racetrack memories is to use redundant heads per-track resulting in multiple copies (potentially erroneous) and solving a specialized version of a sequence reconstruction problem. Using this approach, k-deletion correcting codes of length n, with d heads per-track, with redundancy log log n + 4 were constructed. However, the code construction requires that k ≤ d. For k > d, the best known construction improves slightly over the classic one head deletion code. Here we address the question: What is the best redundancy that can be achieved for a k-deletion code (k is a constant) if the number of heads is fixed at d (due to area limitations)? Our key result is an answer to this question, namely, we construct codes that can correct k deletions, for any k beyond the known limit of d. The code has O(k^4 dlog log n) redundancy for the case when k ≤ 2d − 1. In addition, when k ≥ 2d, the code has 2⌊k/d⌋ log n + o(log n) redundancy.