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

This manuscript presents a construction method for quantum codes capable of correcting multiple deletion errors. By introducing two new alogorithms, the alternating sandwich mapping and the block error locator, the proposed method reduces…

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…

As the global need for large-scale data storage is rising exponentially, existing storage technologies are approaching their theoretical and functional limits in terms of density and energy consumption, making DNA based storage a potential…

The deletion distance between two binary words $u,v \in \{0,1\}^n$ is the smallest $k$ such that $u$ and $v$ share a common subsequence of length $n-k$. A set $C$ of binary words of length $n$ is called a $k$-deletion code if every pair of…

Most large-scale storage systems employ erasure coding to provide resilience against disk failures. Recent work has shown that tuning this redundancy to changes in disk failure rates leads to substantial storage savings. This process…

Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column…

Inversions, also sometimes called reversals, are a major contributor to variation among bacterial genomes, with studies suggesting that those involving small numbers of regions are more likely than larger inversions. Deletions may arise in…

DNA is emerging as an increasingly attractive medium for data storage due to a number of important and unique advantages it offers, most notably the unprecedented durability and density. While the technology is evolving rapidly, the…

When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…

This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol ``$0$'' (referred to as $0$-deletions) and/or the insertions of the symbol ``$0$'' (referred to as…

This paper extends the foundational work of Dollma \emph{et al}. on codes for ordered composite DNA sequences. We consider the general setting with an alphabet of size $q$ and a resolution parameter $k$, moving beyond the binary ($q=2$)…

This paper revisits recent code similarity evaluation metrics, particularly focusing on the application of Abstract Syntax Tree (AST) editing distance in diverse programming languages. In particular, we explore the usefulness of these…

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…

Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…

The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…

Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…

We consider error-correcting coding for DNA-based storage. We model the DNA storage channel as a multi-draw IDS channel where the input data is chunked into $M$ short DNA strands, which are copied a random number of times, and the channel…

We consider error-correcting coding for deoxyribonucleic acid (DNA)-based storage using nanopore sequencing. We model the DNA storage channel as a sampling noise channel where the input data is chunked into $M$ short DNA strands, which are…

The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…

We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…