Related papers: On the Design of Codes for DNA Computing: Secondar…
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…
Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics 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 a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters…
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…
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to…
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…
We study the amount of reliable information that can be stored in a DNA-based storage system composed of short DNA molecules. In this regime, Shomorony and Heckel (2022) put forward a conjecture on the scaling of the number of information…
This work introduces a novel approach to constructing DNA codes from linear codes over a non-chain extension of $\mathbb{Z}_4$. We study $(\text{\textbaro},\mathfrak{d}, \gamma)$-constacyclic codes over the ring…
We present a finite blocklength performance bound for a DNA storage channel with insertions, deletions, and substitutions. The considered bound -- the dependency testing (DT) bound, introduced by Polyanskiy et al. in 2010 -- provides an…
We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. The mathematical basis of the problem is the construction and design of sequences that may be discriminated based on…
In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
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…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
Thanks to computing power increase, the certification and the conception of complex systems relies more and more on simulation. To this end, predictive codes are needed, which have generally to be evaluated in a huge number of input points.…
Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all…
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
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…