Related papers: Function-Correcting Codes for Insertion-Deletion C…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…
Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding…
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…
Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible…
DNA storage systems face significant challenges, including insertion, deletion, and substitution (IDS) errors. Therefore, designing effective synchronization codes, i.e., codes capable of correcting IDS errors, is essential for DNA storage…
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.…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…
In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
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…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions $(\delta=1)$ with an…
When computing systems can tolerate the effects of errors or erasures in their communicated data values, they can trade this tolerance for improved resource efficiency. One method for enabling this tradeoff in the I/O subsystems of…
In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance…
A message composed of packets is transmitted using erasure and channel coding over a fading channel with no feedback. For this scenario, the paper explores the trade-off between the redundancies allocated to the packet-level erasure code…
We study near optimal error correction codes for real-time communication. In our setup the encoder must operate on an incoming source stream in a sequential manner, and the decoder must reconstruct each source packet within a fixed playback…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this…
This paper presents general bounds on the highest achievable rate for list-decodable insertion-deletion codes. In particular, we give novel outer and inner bounds for the highest achievable communication rate of any insertion-deletion code…
We improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an…
Erasure coding is a storage-efficient alternative to replication for achieving reliable data backup in distributed storage systems. During the storage process, traditional erasure codes require a unique source node to create and upload all…