Related papers: Error-Correcting Codes for Nanopore Sequencing
Motivation: New long read sequencers promise to transform sequencing and genome assembly by producing reads tens of kilobases long. However their high error rate significantly complicates assembly and requires expensive correction steps to…
The determination of a patient's DNA sequence can, in principle, reveal an increased risk to fall ill with particular diseases [1,2] and help to design "personalized medicine" [3]. Moreover, statistical studies and comparison of genomes [4]…
Nanopore sequencing of DNA is a single-molecule technique that may achieve long reads, low cost, and high speed with minimal sample preparation and instrumentation. Here, we build on recent progress with respect to nanopore resolution and…
DNA is a leading candidate as the next archival storage media due to its density, durability and sustainability. To read (and write) data DNA storage exploits technology that has been developed over decades to sequence naturally occurring…
Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction…
Motivated by the concept of probe storage, we study the problem of information retrieval using a large array of N nano-mechanical probes, N ~ 4000. At the nanometer scale it is impossible to avoid errors in the positioning of the array,…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
We study error-correcting codes in the space $\mathcal{S}_{n,q}$ of length-$n$ multisets over a $q$-ary alphabet, motivated by permutation channels in which ordering is completely lost and errors act solely by deletions of symbols, i.e., by…
Recent experiments have demonstrated the feasibility of storing digital information in macromolecules such as DNA and protein. However, the DNA storage channel is prone to errors such as deletions, insertions, and substitutions. During the…
The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
In this paper, we develop a new channel model, which we name the $q$-ary partial erasure channel (QPEC). The QPEC has a $q$-ary input, and its output is either the input symbol or a set of $M$ ($2 \le M \le q$) symbols, containing the input…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
In recent years, the emergence of DNA storage systems has led to a widespread focus on the research of codes correcting insertions, deletions, and classic substitutions. During the initial investigation, Levenshtein discovered the VT codes…
Nanopore sequencing offers the ability for real-time analysis of long DNA sequences at a low cost, enabling new applications such as early detection of cancer. Due to the complex nature of nanopore measurements and the high cost of…
The study of functional genomics--particularly in non-model organisms has been dramatically improved over the last few years by use of transcriptomes and RNAseq. While these studies are potentially extremely powerful, a computationally…
DNA nanotechnology uses predictable interactions of nucleic acids to precisely engineer complex nanostructures. Characterizing these self-assembled structures at the single-structure level is crucial for validating their design and…
We study segmented burst-deletion channels motivated by the observation that synchronization errors commonly occur in a bursty manner in real-world settings. In this channel model, transmitted sequences are implicitly divided into…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
We evaluate the performance of small error-correcting codes, which we tailor to hardware platforms of very different connectivity and coherence: on a superconducting processor based on transmon qubits and a spintronic quantum register…