Codes for Correcting t Limited-Magnitude Sticky Deletions
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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 ⌈2t(1-1/p)⌉·⌈log p⌉/log plog(n+1)+O(loglog n), where p is the smallest prime larger than ℓ+1.
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