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The efficient storage of digital data is becoming very challenging over the years due to the exponential increase in the generation of data which can't compete with the existing storage resources. Furthermore, the infrequently accessed data…
We study permutations over the set of $\ell$-grams, that are feasible in the sense that there is a sequence whose $\ell$-gram frequency has the same ranking as the permutation. Codes, which are sets of feasible permutations, protect…
Molecular biology explains function of molecules by their geometrical and electronical structures that are mainly determined by utilization of quantum effects in chemistry. However, further quantum effects are not thought to play any…
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…
This work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems. We study this probability under independent and identically distributed…
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and trade-offs of DNA-based storage systems by introducing a new channel model, which we…
DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards…
We propose coding techniques that limit the length of homopolymers runs, ensure the GC-content constraint, and are capable of correcting a single edit error in strands of nucleotides in DNA-based data storage systems. In particular, for…
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 storage is a promising archival data storage solution to today's big data problem. A DNA storage system encodes and stores digital data with synthetic DNA sequences and decodes DNA sequences back to digital data via sequencing. For…
Charge migration along DNA molecules has attracted scientific interest for over half a century. Reports on possible high rates of charge transfer between donor and acceptor through the DNA, obtained in the last decade from solution…
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…
Researchers in the field of DNA-based chaotic cryptography have recently proposed a set of novel and efficient image encryption algorithms. In this paper, we present a comprehensive summary of those techniques, which are available in the…
A general theoretical framework is put forth to organize and understand various observed phenomena and mathematical relationships in the field of molecular biology. By modeling each cell in eukaryotic organisms as a processor having a…
Since security is one of the most important issues, the evolve of cryptography and cryptographic analysis are considered as the fields of on-going research. The latest development on this field is DNA cryptography. It has emerged after the…
Channels with synchronization errors, such as deletion and insertion errors, are crucial in DNA storage, data reconstruction, and other applications. These errors introduce memory to the channel, complicating its capacity analysis. This…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
We consider the problem of storing and retrieving information from synthetic DNA media. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on their collection of substrings…
Deoxyribonucleic acid (DNA) has emerged as a promising building block for next-generation ultra-high density storage devices. Although DNA has high durability and extremely high density in nature, its potential as the basis of storage…
Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current…