Codes for Correcting t Limited-Magnitude Sticky Deletions

Codes for correcting sticky insertions/deletions and limited-magnitude errors have attracted significant attention due to their applications of flash memories, racetrack memories, and DNA data storage systems. In this paper, we first consider the error type of t sticky deletions with ℓ-limited-magnitude and propose a non-systematic code for correcting this type of error with redundancy 2t(1 − 1/p) • log(n + 1) + O(1), where p is the smallest prime larger than ℓ + 1. Next, we present a systematic code construction with an efficient encoding and decoding algorithm with redundancy $\frac{{\left\lceil {2t(1 - 1/p)} \right\rceil \cdot \left\lceil {\log p} \right\rceil }}{{\log p}}\log (n + 1) + O(\log \log n)$, where p is the smallest prime larger than ℓ + 1.