相关论文: Codes in the Damerau Distance for DNA Storage

DNA is a leading candidate as the next archival storage media due to its density, durability and sustainability. To read (and write) data DNA storage exploits technology that has been developed over decades to sequence naturally occurring…

An edit distance is a measure of the minimum cost sequence of edit operations to transform one structure into another. Edit distance is most commonly encountered within the context of strings, where Wagner and Fischer's string edit distance…

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…

Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…

In [1], the authors proposed a new model of DNA storage system that integrates all three steps of retrieval and introduced the concept of DNA-correcting codes, which guarantees that the output of the storage system can be decoded to the…

Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…

DNA synthesis is considered as one of the most expensive components in current DNA storage systems. In this paper, focusing on a common synthesis machine, which generates multiple DNA strands in parallel following a fixed supersequence,we…

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 normalized edit distance is one of the distances derived from the edit distance. It is useful in some applications because it takes into account the lengths of the two strings compared. The normalized edit distance is not defined in…

The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…

Storing information in DNA molecules is of great interest because of its advantages in longevity, high storage density, and low maintenance cost. A key step in the DNA storage pipeline is to efficiently cluster the retrieved DNA sequences…

Racetrack memory is a new technology which utilizes magnetic domains along a nanoscopic wire in order to obtain extremely high storage density. In racetrack memory, each magnetic domain can store a single bit of information, which can be…

The biggest challenge when using DNA as a storage medium is maintaining its stability. The relative occurrence of Guanine (G) and Cytosine (C) is essential for the longevity of DNA. In addition to that, reverse complementary base pairs…

The rapid development of DNA storage has brought the deletion and insertion channel, once again, to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is…

The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit…

Motivated by applications in DNA storage, we study a setting in which strings are affected by tandem-duplication errors. In particular, we look at two settings: disjoint tandem-duplication errors, and equal-length tandem-duplication errors.…

The rank modulation scheme has been proposed for efficient writing and storing data in non-volatile memory storage. Error-correction in the rank modulation scheme is done by considering permutation codes. In this paper we consider codes in…

In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…

Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…

A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…