相关论文: Equivalence of Insertion/Deletion Correcting Codes…
This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an $n\times n$ array can experience deletions of rows and columns. These deletion errors are referred to as…
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…
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…
We consider the (one-dimensional) array counterpart of contextual as well as insertion and deletion string grammars and consider the operations of array insertion and deletion in array grammars. First we show that the emptiness problem for…
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we further study this intriguing mathematical problem,…
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…
Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that…
Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating developments of channel codes that can correct such errors. In…
Construction of capacity achieving deletion correcting codes has been a baffling challenge for decades. A recent breakthrough by Brakensiek $et~al$., alongside novel applications in DNA storage, have reignited the interest in this…
Locality enables storage systems to recover failed nodes from small subsets of surviving nodes. The setting where nodes are partitioned into subsets, each allowing for local recovery, is well understood. In this work we consider a…
Quantum synchronisation errors are a class of quantum errors that change the number of qubits in a quantum system. The classical error correction of synchronisation errors has been well-studied, including an insertion-deletion equivalence…
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…
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…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
Already in the 1960s, Levenshtein and others studied error-correcting codes that protect against synchronization errors, such as symbol insertions and deletions. However, despite significant efforts, progress on designing such codes has…
This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting…
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…
Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language…
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…