Related papers: Low-redundancy codes for correcting multiple short…
The rapidly improving performance of modern hardware renders convolutional codes obsolete, and allows for the practical implementation of more sophisticated correction codes such as low density parity check (LDPC) and turbo codes (TC). Both…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics,…
Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate…
This study explores the self-synchronization problem in DNA coding, specifically addressing single-deletion errors without using delimiters between codewords. We aim to identify the beginning of each codeword without using delimiters,…
Distributed storage systems support failures of individual devices by the use of replication or erasure correcting codes. While erasure correcting codes offer a better storage efficiency than replication for similar fault tolerance, they…
While achieving a compression ratio of 2.0 bits/base, the new algorithm codes non-N bases in fixed length. It dramatically reduces the time of coding and decoding than previous DNA compression algorithms and some universal compression…
The substring edit error is the operation of replacing a substring $u$ of $x$ with another string $v$, where the lengths of $u$ and $v$ are bounded by a given constant $k$. It encompasses localized insertions, deletions, and substitutions…
DNA-based data storage has been attracting significant attention due to its extremely high data storage density, low power consumption, and long duration compared to conventional data storage media. Despite the recent advancements in DNA…
We offer a theoretical design of new systems that show promise for digital biochemical computing, including realizations of error correction by utilizing redundancy, as well as signal rectification. The approach includes information…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
While most current high-throughput DNA sequencing technologies generate short reads with low error rates, emerging sequencing technologies generate long reads with high error rates. A basic question of interest is the tradeoff between read…
Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for…
This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by $t$-criss-cross deletions defined as any combination…
DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the \emph{coverage depth problem} in practical scenarios, exploring optimal…
High read depth can be used to assemble short sequence repeats. The existing genome assemblers fail in repetitive regions of longer than average read. I propose a new algorithm for a DNA assembly which uses the relative frequency of reads…
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to…
The yearly global production of data is growing exponentially, outpacing the capacity of existing storage media, such as tape and disk, and surpassing our ability to store it. DNA storage - the representation of arbitrary information as…
This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…
A method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…