Related papers: On the Reverse-Complement String-Duplication Syste…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
Information capacity of a symbol sequence is a measure of the unexpectedness of a continuation of given string of symbols. Continuation of a string is determined through the maximum entropy of the reconstructed frequency dictionary; the…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
We present an algorithm for building the extended BWT (eBWT) of a string collection from its grammar-compressed representation. Our technique exploits the string repetitions captured by the grammar to boost the computation of the eBWT.…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
The Shortest Common Superstring (SCS) problem is a fundamental task in sequence analysis. In genome assembly, however, the double-stranded nature of DNA implies that each fragment may occur either in its original orientation or as its…
DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…
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…
The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…
String matching is a fundamental problem in algorithm. This study examines the development and construction of two reversible string-matching algorithms: a naive string-matching algorithm and the Rabin-Karp algorithm. The algorithms are…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
DNA codes have many applications, such as in data storage, DNA computing, etc. Good DNA codes have large sizes and satisfy some certain constraints. In this paper, we present a new construction method for reversible DNA codes. We show that…
This paper studies codes that correct bursts of deletions. Namely, a code will be called a $b$-burst-deletion-correcting code if it can correct a deletion of any $b$ consecutive bits. While the lower bound on the redundancy of such codes…
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…
In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical attainability results typically rely on compactness of the…
In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we…
A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
We consider the problem of constructing a code capable of correcting a single long tandem duplication error of variable length. As the main contribution of this paper, we present a $q$-ary efficiently encodable code of length $n+1$ and…
The problem of storing large amounts of information safely for a long period of time has become essential. One of the most promising new data storage mediums are the polymer-based data storage systems, like the DNA-storage system. These…