Related papers: The sequence reconstruction problem for permutatio…
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…
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 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…
Levenshtein first introduced the sequence reconstruction problem in $2001$. In the realm of combinatorics, the sequence reconstruction problem is equivalent to determining the value of $N(n,d,t)$, which represents the maximum size of the…
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.…
The sequence reconstruction problem asks for the recovery of a sequence from multiple noisy copies, where each copy may contain up to $r$ errors. In the case of permutations on \(n\) letters under the Hamming metric, this problem is closely…
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…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains $N$ noisy outputs of the codeword. We study the problem of…
In the paper, the Levenshtein's sequence reconstruction problem is considered in the case where at most $t$ substitution errors occur in each of the $N$ channels and the decoder outputs a list of length $\mathcal{L}$. Moreover, it is…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study…
The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely…
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…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common…
The sequence reconstruction problem for insertion/deletion channels has attracted significant attention owing to their applications recently in some emerging data storage systems, such as racetrack memories, DNA-based data storage. Our goal…
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.…
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…
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…
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. Motivated 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…
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…