相关论文: Optimal Codes Correcting a Single Indel / Edit for…

Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai \emph{et al}. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is…

Motivated by DNA-based data storage, we investigate a system where digital information is stored in an unordered set of several vectors over a finite alphabet. Each vector begins with a unique index that represents its position in the whole…

In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors…

Due to its higher data density, longevity, energy efficiency, and ease of generating copies, DNA is considered a promising storage technology for satisfying future needs. However, a diverse set of errors including deletions, insertions,…

DNA is a promising storage medium, but its stability and occurrence of Indel errors pose a significant challenge. The relative occurrence of Guanine(G) and Cytosine(C) in DNA is crucial for its longevity, and reverse complementary base…

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…

The problem of correcting deletions and insertions has recently received significantly increased attention due to the DNA-based data storage technology, which suffers from deletions and insertions with extremely high probability. In this…

We study the combination of two recent coding approaches, in the context of DNA based data storage. Composite DNA alphabets leverage properties of the DNA synthesis and sequencing process. A composite symbol does not represent a single…

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…

To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit…

In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…

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…

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, dating back to 1965, are zero-error single deletion $(\delta=1)$…

We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965…

This study explores the self-synchronization problem in DNA coding, specifically addressing single-deletion errors without using delimiters between codewords. We aim to identify the beginning of each codeword without using delimiters,…

A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…

We introduce synchronization strings as a novel way of efficiently dealing with synchronization errors, i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to deal with than commonly considered…

The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes…

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…

As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…