Related papers: Fundamental Bounds and Approaches to Sequence Reco…
In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…
Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each…
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…
Given a sequence $s_1$ of $n$ letters drawn i.i.d. from an alphabet of size $\sigma$ and a mutated substring $s_2$ of length $m < n$, we often want to recover the mutation history that generated $s_2$ from $s_1$. Modern sequence aligners…
Molecular phylogenetic techniques do not generally account for such common evolutionary events as site insertions and deletions (known as indels). Instead tree building algorithms and ancestral state inference procedures typically rely on…
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern…
DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are…
At the core of high throughput DNA sequencing platforms lies a bio-physical surface process that results in a random geometry of clusters of homogenous short DNA fragments typically hundreds of base pairs long - bridge amplification. The…
Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error…
We consider the correction of errors from nucleotide sequences produced by next-generation targeted amplicon sequencing. The next-generation sequencing (NGS) platforms can provide a great deal of sequencing data thanks to their high…
This work studies problems in data reconstruction, an important area with numerous applications. In particular, we examine the reconstruction of binary and non-binary sequences from synchronization (insertion/deletion-correcting) codes.…
Synthetic DNA can in principle be used for the archival storage of arbitrary data. Because errors are introduced during DNA synthesis, storage, and sequencing, an error-correcting code (ECC) is necessary for error-free recovery of the data.…
The problem of reconstructing a sequence from the set of its length-$k$ substrings has received considerable attention due to its various applications in genomics. We study an uncoded version of this problem where multiple random sources…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
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…
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…
Recent advances in DNA sequencing technology and DNA storage systems have rekindled the interest in deletion channels. Multiple recent works have looked at variants of sequence reconstruction over a single and over multiple deletion…
The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by deletions, insertions, and substitutions. This problem arises in applications such as DNA data storage, a…
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…
DNA is an attractive candidate for data storage. Its millennial durability and nanometer scale offer exceptional data density and longevity. Its relevance to medical applications also drives advances in DNA-related biotechnology. To protect…