scholarly journals A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1592
Author(s):  
Thi-Huong Khuat ◽  
Sunghwan Kim
Keyword(s):  
Error Correction ◽  
Data Storage ◽  
Upper Bounds ◽  
Code Design ◽  
Lower And Upper Bounds ◽  
Decoding Algorithms ◽  
Quaternary Code ◽  
Quaternary Codes ◽  
Dna Storage ◽  
Dna Strands

Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.

scholarly journals Promiscuous molecules for smarter file operations in DNA-based data storage

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kyle J. Tomek ◽  
Kevin Volkel ◽  
Elaine W. Indermaur ◽  
James M. Tuck ◽  
Albert J. Keung
Keyword(s):  
Data Storage ◽  
Data Access ◽  
Molecular Architecture ◽  
Biomolecular Structure ◽  
Jpeg Images ◽  
Storage Media ◽  
Dna Storage ◽  
Dna Strands ◽  
Background Database ◽  
Organizational Features

AbstractDNA holds significant promise as a data storage medium due to its density, longevity, and resource and energy conservation. These advantages arise from the inherent biomolecular structure of DNA which differentiates it from conventional storage media. The unique molecular architecture of DNA storage also prompts important discussions on how data should be organized, accessed, and manipulated and what practical functionalities may be possible. Here we leverage thermodynamic tuning of biomolecular interactions to implement useful data access and organizational features. Specific sets of environmental conditions including distinct DNA concentrations and temperatures were screened for their ability to switchably access either all DNA strands encoding full image files from a GB-sized background database or subsets of those strands encoding low resolution, File Preview, versions. We demonstrate File Preview with four JPEG images and provide an argument for the substantial and practical economic benefit of this generalizable strategy to organize data.

scholarly journals On Models and Capacity Bounds for DNA-based Storage Channels

2021 ◽  
Author(s):  
Zihui Yan ◽  
Cong Liang
Keyword(s):  
Data Storage ◽  
Storage System ◽  
Synchronization Error ◽  
Dna Molecules ◽  
Capacity Limits ◽  
Dna Storage ◽  
Capacity Bounds ◽  
Dna Strands ◽  
Term Data

In recent years, DNA-based systems have become a promising medium for long-term data storage. There are two layers of errors in DNA-based storage systems. The first is the dropouts of the DNA strands, which has been characterized in the shuffling-sampling channel. The second is insertions, deletions, and substitutions of nucleotides in individual DNA molecules. In this paper, we describe a DNA noisy synchronization error channel to characterize the errors in individual DNA molecules. We derive non-trivial lower and upper capacity bounds of the DNA noisy synchronization error channel based on information theory. By cascading these two channels, we provide theoretical capacity limits of the DNA storage system. These results reaffirm that DNA is a reliable storage medium with high storage density potential.

scholarly journals On Models and Capacity Bounds for DNA-based Storage Channels

2021 ◽  
Author(s):  
Zihui Yan ◽  
Cong Liang
Keyword(s):  
Data Storage ◽  
Storage System ◽  
Synchronization Error ◽  
Dna Molecules ◽  
Capacity Limits ◽  
Dna Storage ◽  
Capacity Bounds ◽  
Dna Strands ◽  
Term Data

In recent years, DNA-based systems have become a promising medium for long-term data storage. There are two layers of errors in DNA-based storage systems. The first is the dropouts of the DNA strands, which has been characterized in the shuffling-sampling channel. The second is insertions, deletions, and substitutions of nucleotides in individual DNA molecules. In this paper, we describe a DNA noisy synchronization error channel to characterize the errors in individual DNA molecules. We derive non-trivial lower and upper capacity bounds of the DNA noisy synchronization error channel based on information theory. By cascading these two channels, we provide theoretical capacity limits of the DNA storage system. These results reaffirm that DNA is a reliable storage medium with high storage density potential.

scholarly journals NOREC4DNA: using near-optimal rateless erasure codes for DNA storage

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Peter Michael Schwarz ◽  
Bernd Freisleben
Keyword(s):  
Data Storage ◽  
Dna Sequences ◽  
Storage Systems ◽  
High Capacity ◽  
Digital Data ◽  
Erasure Codes ◽  
Software Framework ◽  
Digital Information ◽  
Dna Storage ◽  
Dna Strands

Abstract Background DNA is a promising storage medium for high-density long-term digital data storage. Since DNA synthesis and sequencing are still relatively expensive tasks, the coding methods used to store digital data in DNA should correct errors and avoid unstable or error-prone DNA sequences. Near-optimal rateless erasure codes, also called fountain codes, are particularly interesting codes to realize high-capacity and low-error DNA storage systems, as shown by Erlich and Zielinski in their approach based on the Luby transform (LT) code. Since LT is the most basic fountain code, there is a large untapped potential for improvement in using near-optimal erasure codes for DNA storage. Results We present NOREC4DNA, a software framework to use, test, compare, and improve near-optimal rateless erasure codes (NORECs) for DNA storage systems. These codes can effectively be used to store digital information in DNA and cope with the restrictions of the DNA medium. Additionally, they can adapt to possible variable lengths of DNA strands and have nearly zero overhead. We describe the design and implementation of NOREC4DNA. Furthermore, we present experimental results demonstrating that NOREC4DNA can flexibly be used to evaluate the use of NORECs in DNA storage systems. In particular, we show that NORECs that apparently have not yet been used for DNA storage, such as Raptor and Online codes, can achieve significant improvements over LT codes that were used in previous work. NOREC4DNA is available on https://github.com/umr-ds/NOREC4DNA. Conclusion NOREC4DNA is a flexible and extensible software framework for using, evaluating, and comparing NORECs for DNA storage systems.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number
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