Related papers: Optimal Reconstruction Codes for Deletion Channels
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance…
Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable…
The trace reconstruction problem studies the number of noisy samples needed to recover an unknown string $\boldsymbol{x}\in\{0,1\}^n$ with high probability, where the samples are independently obtained by passing $\boldsymbol{x}$ through a…
We construct deletion error-correcting codes in the oblivious model, where errors are adversarial but oblivious to the encoder's randomness. Oblivious errors bridge the gap between the adversarial and random error models, and are motivated…
We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on…
In this paper, for any fixed positive integers $t$ and $q>2$, we construct $q$-ary codes correcting a burst of at most $t$ deletions with redundancy $\log n+8\log\log n+o(\log\log n)+\gamma_{q,t}$ bits and near-linear encoding/decoding…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
DNA has immense potential as an emerging data storage medium. The principle of DNA storage is the conversion and flow of digital information between binary code stream, quaternary base, and actual DNA fragments. This process will inevitably…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbolwise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
In this paper, we construct systematic $q$-ary two-deletion correcting codes and burst-deletion correcting codes, where $q\geq 2$ is an even integer. For two-deletion codes, our construction has redundancy $5\log n+O(\log q\log\log n)$ and…
The problem of reconstructing a string from its error-prone copies, the trace reconstruction problem, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction,…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
Trace reconstruction is the problem of learning an unknown string $x$ from independent traces of $x$, where traces are generated by independently deleting each bit of $x$ with some deletion probability $q$. In this paper, we initiate the…
An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided,…
We consider the problem of storing and retrieving information from synthetic DNA media. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on their collection of substrings…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
As the global need for large-scale data storage is rising exponentially, existing storage technologies are approaching their theoretical and functional limits in terms of density and energy consumption, making DNA based storage a potential…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for unique string…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…