Related papers: Sequence Reconstruction for Sticky Insertion/Delet…
The sequence reconstruction problem involves a model where a sequence is transmitted over several identical channels. This model investigates the minimum number of channels required for the unique reconstruction of the transmitted sequence.…
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…
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…
The Levenshtein sequence reconstruction problem studies the reconstruction of a transmitted sequence from multiple erroneous copies of it. A fundamental question in this field is to determine the minimum number of erroneous copies required…
The central problem in sequence reconstruction is to find the minimum number of distinct channel outputs required to uniquely reconstruct the transmitted sequence. According to Levenshtein's work in 2001, this number is determined by the…
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…
In coding theory, handling errors that occur when symbols are inserted or deleted from a transmitted message is a long-standing challenge. Optimising redundancy for insertion and deletion channels remains a key open problem with significant…
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in…
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.…
The sequence reconstruction problem was proposed by Levenshtein in 2001. In this model, a sequence from a code is transmitted over several channels, and the decoder receives the distinct outputs from each channel. The main problem is to…
In this paper, we consider the Levenshtein's sequence reconstruction problem in the case where the transmitted codeword is chosen from $\{0,1\}^n$ and the channel can delete up to $t$ symbols from the transmitted codeword. We determine the…
Nanopore sequencers are emerging as promising new platforms for high-throughput sequencing. As with other technologies, sequencer errors pose a major challenge for their effective use. In this paper, we present a novel information theoretic…
This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…
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…
This paper studies the sequence reconstruction problem for a channel inspired by protein identification. We introduce a coloring channel, where a sequence is transmitted through a channel that deletes all symbols not belonging to a fixed…
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…
In this paper, we study how often unique decoding from $t$ insertions or $t$ deletions occurs for error correcting codes. Insertions and deletions frequently occur in synchronization problems and DNA, a medium which is beginning to be used…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
In the Levenshtein's sequence reconstruction problem a codeword is transmitted through $N$ channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a…
V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the model where the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume…