Related papers: DNA Codes that Avoid Secondary Structures
Because of the limitations of classical silicon based computational technology, several alternatives to traditional method in form of unconventional computing have been proposed. In this paper we will focus on DNA computing which is showing…
The DNA storage channel is considered, in which the $M$ Deoxyribonucleic acid (DNA) molecules comprising each codeword are stored without order, sampled $N$ times with replacement, and then sequenced over a discrete memoryless channel. For…
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…
Semiconstrained systems were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
The present paper is devoted to the study of the combinatorics of 216 maximal $C^3$ circular codes --- a particular type of structure arising in the analysis of genomic sequences. Their circularity property is believed to be intimately…
This paper presents a novel method to segment/decode DNA sequences based on n-grams statistical language model. Firstly, we find the length of most DNA 'words' is 12 to 15 bps by analyzing the genomes of 12 model species. Then we design an…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
The coverage depth problem in DNA data storage is about computing the expected number of reads needed to recover all encoded strands. Given a generator matrix of a linear code, this quantity equals the expected number of randomly drawn…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
In this paper, we develop the theory for constructing DNA cyclic codes of odd length over $R=\Z_4[u]/\langle u^2-1 \rangle$ based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic codes of…
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…
DNA storage technology offers new possibilities for addressing massive data storage due to its high storage density, long-term preservation, low maintenance cost, and compact size. To improve the reliability of stored information, base…
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…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
There exists many complicated $k$-noncrossing pseudoknot RNA structures in nature based on some special conditions. The special characteristic of RNA structures gives us great challenges in researching the enumeration, prediction and the…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…
Current techniques in sequencing a genome allow a service provider (e.g. a sequencing company) to have full access to the genome information, and thus the privacy of individuals regarding their lifetime secret is violated. In this paper, we…
In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare…