Publications

DNA labeling is a tool in molecular biology and biotechnology to visualize, detect, and study DNA at the molecular level. In this process, a DNA molecule is labeled by a set of specific patterns, referred to as labels, and is then imaged. The resulting image is modeled as an (ℓ+1)-ary sequence, where ℓ is the number of labels, in which any non-zero symbol indicates the appearance of the corresponding label in the DNA molecule. The labeling capacity refers to the maximum information rate that can be achieved by the labeling process for any given set of labels. The main goal of this paper is to study the minimum number of labels of the same length required to achieve the maximum labeling capacity of 2 for DNA sequences or log2q for an arbitrary alphabet of size q. The solution to this problem requires the study of path unique subgraphs of the de Bruijn graph with the largest number of edges and we provide upper and lower bounds on this value.

This paper studies the adversarial torn-paper channel. This problem is motivated by applications in DNA data storage where the DNA strands that carry the information may break into smaller pieces that are received out of order. Our model extends the previously researched probabilistic setting to the worst-case. We deve lop code constructions for any parameters of the channel for which non-vanishing asymptotic rate is possible and show that our constructions achieve optimal asymptotic rate while allowing for efficient encoding and decoding. Finally, we extend our results to related settings included multi-strand storage, presence of substitution errors, or incomplete coverage.

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a scenario where the sender transmits a codeword from some codebook, and the receiver obtains N noisy outputs of the codeword. We study the problem of efficient reconstruction using N outputs that are corrupted by substitutions. Specifically, for the ubiquitous Reed-Solomon codes, we adapt the Koetter-Vardy soft-decoding algorithm, pre- senting a reconstruction algorithm capable of correcting beyond Johnson radius. Furthermore, the algorithm uses O(n N) field operations, where n is the codeword length.

Reliability is an inherent challenge for the emerging nonvolatile technology of racetrack memories, and there exists a fundamental relationship between codes designed for racetrack memories and codes with constrained periodicity. Previous works have sought to construct codes that avoid periodicity in windows, yet have either only provided existence proofs or required high redundancy. This paper provides the first constructions for avoiding periodicity that are both efficient (average-linear time) and with low redundancy (near the lower bound). The proposed algorithms are based on iteratively repairing windows which contain periodicity until all the windows are valid. Intuitively, such algorithms should not converge as there is no monotonic progression; yet, we prove convergence with average-linear time complexity by exploiting subtle properties of the encoder. Overall, we both provide constructions that avoid periodicity in all windows, and we also study the cardinality of such constraints.

Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost stands at roughly 1.3K/TB, which is dramatically more expensive than reading from existing archival storage solutions today. In this work, we aim to reduce not only the cost but also the latency of DNA storage by studying the DNA coverage depth problem, which aims to reduce the required number of reads to retrieve information from the storage system. Under this framework, our main goal is to understand how to optimally pair an error-correcting code with a given retrieval algorithm to minimize the sequencing coverage depth, while guaranteeing retrieval of the information with high probability. Additionally, we study the DNA coverage depth problem under the random-access setup.

DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the coverage depth problem in practical scenarios, exploring optimal error-correcting code pairings with DNA storage systems to minimize coverage depth. Conducted within random access settings, the study provides theoretical analyses and experimental simulations to examine the expectation and probability distribution of samples needed for files recovery. Structured into sections covering definitions, analyses, lower bounds, and comparative evaluations of coding schemes, the paper unveils insights into effective coding schemes for optimizing DNA storage systems.

We address the challenge of optimizing the capacity-achieving input distribution for a multinomial channel under the constraint of limited input support size, which is a crucial aspect in the design of DNA storage systems. We propose an algorithm that further elaborates the Multidimensional Dynamic Assignment Blahut-Arimoto (M-DAB) algorithm. Our proposed algorithm integrates variational autoencoder for determining the optimal locations of input distribution, into the alternating optimization of the input distribution locations and weights.

Motivation

Optical genome mapping (OGM) is a technique that extracts partial genomic information from optically imaged and linearized DNA fragments containing fluorescently labeled short sequence patterns. This information can be used for various genomic analyses and applications, such as the detection of structural variations and copy-number variations, epigenomic profiling, and microbial species identification. Currently, the choice of labeled patterns is based on the available biochemical methods and is not necessarily optimized for the application.

Results

In this work, we develop a model of OGM based on information theory, which enables the design of optimal labeling patterns for specific applications and target organism genomes. We validated the model through experimental OGM on human DNA and simulations on bacterial DNA. Our model predicts up to 10-fold improved accuracy by optimal choice of labeling patterns, which may guide future development of OGM biochemical labeling methods and significantly improve its accuracy and yield for applications such as epigenomic profiling and cultivation-free pathogen identification in clinical samples.

Labeling of DNA molecules is a fundamental technique for DNA visualization and analysis. This process was mathematically modeled in [1], where the received sequence indicates the positions of the used labels. In this work, we develop error correcting codes for labeled DNA sequences, establishing bounds and constructing explicit systematic encoders for single substitution, insertion, and deletion errors. We focus on two cases: (1) using the complete set of length-two labels and (2) using the minimal set of length-two labels that ensures the recovery of DNA sequences from their labeling for ‘almost’ all DNA sequences.

Recent experiments have shown that the capacity of DNA storage systems may be significantly increased by synthesizing composite DNA letters. In this work, we model a DNA storage channel with composite inputs as a multinomial channel, and propose an optimization algorithm for its capacity achieving input distribution, for an arbitrary number of output reads. The algorithm is termed multidimensional dynamic assignment Blahut-Arimoto (M-DAB), and is a generalized version of the DAB algorithm, proposed by Wesel et al. [1] developed for the binomial channel. We also empirically observe a scaling law behavior of the capacity as a function of the support size of the capacity-achieving input distribution.

DNA labeling is a powerful tool in molecular biology and biotechnology that allows for the visualization, detection, and study of DNA at the molecular level. Under this paradigm, a DNA molecule is being labeled by specific k patterns and is then imaged. Then, the resulting image is modeled as a (k+1) -ary sequence in which any non-zero symbol indicates on the appearance of the corresponding label in the DNA molecule. The primary goal of this work is to study the labeling capacity, which is defined as the maximal information rate that can be obtained using this labeling process. The labeling capacity is computed for almost any pattern of a single label and several results for multiple labels are provided as well. Moreover, we provide the optimal minimal number of labels of length one or two, over any alphabet of size q, that are needed in order to achieve the maximum labeling capacity of log2(q) . Lastly, we discuss the maximal labeling capacity that can be achieved using a certain number of labels of length two.

DNA labeling is a powerful tool in molecular biology and biotechnology that allows for the visualization, detection, and study of DNA at the molecular level. Under this paradigm, a DNA molecule is being labeled by specific k patterns and is then imaged. Then, the resulted image is modeled as a (k +1)-ary sequence in which any non-zero symbol indicates on the appearance of the corresponding label in the DNA molecule. The primary goal of this work is to study the labeling capacity, which is defined as the maximal information rate that can be obtained using this labeling process. The labeling capacity is computed for any single label and several results are provided for multiple labels as well. Moreover, we provide the optimal minimal number of labels of length one or two that are needed in order to gain labeling capacity of 2.

In this work we consider a generalization of the well-studied problem of coding for “stuck-at” errors, which we refer to as “strong stuck-at” codes. In the traditional framework of stuck-at codes, the task involves encoding a message into a one-dimensional binary vector. However, a certain number of the bits in this vector are `frozen’, meaning they are fixed at a predetermined value and cannot be altered by the encoder. The decoder, aware of the proportion of frozen bits but not their specific positions, is responsible for deciphering the intended message. We consider a more challenging version of this problem where the decoder does not even know the fraction of frozen bits. We construct explicit and efficient encoding and decoding algorithms that get arbitrarily close to capacity in this scenario. Furthermore, to the best of our knowledge, our construction is the first fully explicit construction of stuck-at codes that approaches capacity.

This paper presents a novel approach to address the constrained coding challenge of generating almost-balanced sequences. While strictly balanced sequences have been well studied in the past, the problem of designing efficient algorithms with small redundancy, preferably constant or even a single bit, for almost balanced sequences has remained unsolved. A sequence is ε(n)-almost balanced if its Hamming weight is between 0.5n±ε(n). It is known that for any algorithm with a constant number of bits, ε(n) has to be in the order of Θ(√n), with O(n) average time complexity. However, prior solutions with a single redundancy bit required ε(n) to be a linear shift from n/2. Employing an iterative method and arithmetic coding, our emphasis lies in constructing almost balanced codes with a single redundancy bit. Notably, our method surpasses previous approaches by achieving the optimal balanced order of Θ(√n). Additionally, we extend our method to the non-binary case considering q-ary almost polarity-balanced sequences for even q, and almost symbol-balanced for q=4. Our work marks the first asymptotically optimal solutions for almost-balanced sequences, for both, binary and non-binary alphabet.

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, every composite symbols does not store a single nucleotide but a mixture of the four DNA nucleotides. In the first problem, our goal is study how to carefully choose a fixed number of mixtures of the DNA nucleotides such that the decoding probability by the maximum likelihood decoder is maximized. The second problem studies the expected number of strand reads in order to decode a composite strand or a group of composite strands.

Motivation Recent years have seen a growing number and an expanding scope of studies using synthetic oligo libraries for a range of applications in synthetic biology. As experiments are growing by numbers and complexity, analysis tools can facilitate quality control and support better assessment and inference. Results We present a novel analysis tool, called SOLQC, which enables fast and comprehensive analysis of synthetic oligo libraries, based on NGS analysis performed by the user. SOLQC provides statistical information such as the distribution of variant representation, different error rates and their dependence on sequence or library properties. SOLQC produces graphical reports from the analysis, in a flexible format. We demonstrate SOLQC by analyzing literature libraries. We also discuss the potential benefits and relevance of the different components of the analysis.

Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While fixed constraints (e.g., a fixed set of substrings may not appear in transmitted messages) have a general optimal solution, there is increasing demand for supporting parametric constraints that are dependent on the message length and portray some property that the substrings must satisfy (e.g., no log (n) consecutive zeros). Several works have tackled such parametric constraints through iterative algorithms following the sequence-replacement approach, yet this approach requires complex constraint-specific properties to guarantee convergence through monotonic progression. In this paper, we propose a universal framework for tackling any parametric constraint problem with far fewer requirements, through a simple iterative algorithm. By reducing an execution of this iterative algorithm to an acyclic graph traversal, we prove a surprising result that guarantees convergence with efficient average time complexity even without requiring any monotonic progression. We demonstrate how to apply this algorithm to the run-length-limited, minimal Hamming weight, local almost-balanced Hamming weight constraints, as well as repeat-free and secondary-structure constraints. Overall, this framework enables state-of-the-art results with minimal effort.