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Codes Correcting a Burst of Deletions or Insertions
TLDR
The models of insertions and deletions are equivalent and thus it is enough to study codes correcting a burst of deletions and derive a non-asymptotic upper bound on the size of these codes.
Portable and Error-Free DNA-Based Data Storage
TLDR
This work represents the only known random access DNA-based data storage system that uses error-prone nanopore sequencers, while still producing error-free readouts with the highest reported information rate/density.
Constructions of partial MDS codes over small fields
TLDR
A family of PMDS codes with field size O(max{m, nr+s}s) is presented and can correct erasure patterns consisting of r erasures in each row together with s more erasures anywhere in the array.
Optimal Systematic t-Deletion Correcting Codes
TLDR
This paper proposes a systematic t-deletion correcting code construction that achieves 4t log n + o(log n) bits of redundancy, which is asymptotically within a factor of 4 from being optimal.
Codes correcting erasures and deletions for rank modulation
TLDR
The main approach in tackling problems is to build upon the existing works of error-correcting codes in the three metrics mentioned above and leverage them in order to construct codes in each model of deletions and erasures.
Coded Trace Reconstruction
TLDR
This work begins the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads corrupted by edit errors, and begins by analyzing marker-based code-constructions coupled with worst-case trace reconstruction algorithms.
Non-binary WOM-codes for multilevel flash memories
TLDR
A new class of codes is introduced, called level distance WOM-codes, which mitigate the difficulty of programming a flash memory cell by eliminating all small-magnitude level increases and is presented how to construct such codes and state an upper bound on their sum-rate.
Tackling intracell variability in TLC Flash through tensor product codes
TLDR
A mathematical model is proposed that captures the intracell variability, which is manifested by certain patterns of bit-errors of TLC (three bits per cell) Flash, and error correction codes are constructed for this model based upon generalized tensor product codes.
Codes in the Damerau Distance for Deletion and Adjacent Transposition Correction
TLDR
The new problem of code design in the Damerau metric is introduced, motivated by applications in DNA-based storage, and constructions for joint block deletion and adjacent block transposition error-correcting codes are provided.
Dynamic Threshold Schemes for Multi-Level Non-Volatile Memories
TLDR
This paper provides a general scheme to compute and apply dynamic thresholds and derive performance bounds and develops limited-magnitude error-correcting codes tailored to take advantage of dynamic thresholds.
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