The DNA Storage Channel: Capacity and Error Probability

Weinberger, Nir; Merhav, Neri

doi:10.48550/arxiv.2109.12549

Cited by 5 publications

(7 citation statements)

References 34 publications

(156 reference statements)

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“…The capacity of multi-draw DNA storage channels where the noisy channel p(y|x) is an arbitrary discrete memoryless channel recently received a careful treatment by Weinberger and Merhav [WM21]. The paper provides a new lower bound for general multi-draw DNA storage channels that is based on a random coding argument and holds for all values of β > 1, unlike the achievability arguments for Theorems 6 and 7, which only cover specific discrete memoryless channels.…”

Section: General Discrete Memoryless Channelsmentioning

confidence: 99%

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Information-Theoretic Foundations of DNA Data Storage

Shomorony

Heckel

2022

FNT in Communications and Information Theory

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Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Natural DNA more than 700.000 years old has been recovered, and about 5 grams of DNA can in principle hold a Zetabyte of digital information, orders of magnitude more than what is achieved on conventional storage media. Thanks to rapid technological advances, DNA storage is becoming practically feasible, as demonstrated by a number of experimental storage systems, making it a promising solution for our society's increasing need of data storage.While in living things, DNA molecules can consist of millions of nucleotides, due to technological constraints, in practice, data is stored on many short DNA molecules, which are preserved in a DNA pool and cannot be spatially ordered. Moreover, imperfections in sequencing, synthesis, and handling, as well as DNA decay during storage, introduce random noise into the system, making the task of reliably storing and retrieving information in DNA challenging.This unique setup raises a natural information-theoretic question: how much information can be reliably stored on and reconstructed from millions of short noisy sequences? The goal of this monograph is to address this question by discussing the fundamental limits of storing information on DNA. Motivated by current technological constraints on DNA synthesis and sequencing, we propose a probabilistic channel model that captures three key distinctive aspects of the DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered fashion; (2) the molecules are corrupted by noise and (3) the data is read by randomly sampling from the DNA pool. Our goal is to investigate the impact of each of these key aspects on the capacity of the DNA storage system. Rather than focusing on coding-theoretic considerations and computationally efficient encoding and decoding, we aim to build an information-theoretic foundation for the analysis of these channels, developing tools for achievability and converse arguments.

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Section: General Discrete Memoryless Channelsmentioning

confidence: 99%

“…as long as β > β cr , where β cr can be explicitly computed [WM21], and C n is the capacity of the modulo-additive channel with n draws. For the special case X = {0, 1}, the modulo-additive channel reduces to the BSC, and the result in Theorem 7 is recovered, but with a weaker requirement on p and β.…”

Section: General Discrete Memoryless Channelsmentioning

confidence: 99%

Information-Theoretic Foundations of DNA Data Storage

Shomorony

Heckel

2022

FNT in Communications and Information Theory

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“…Multiple channel models have recently been suggested and studied based on this property. An assumption of overlap in read substrings and (near) uniform coverage leads to the problem of string reconstruction from substring composition [3], [4], [7], [13], [21], [22], [27], [29]; on the contrary, assuming no overlap in read substrings leads to the torn-paper problem [23], [25], [30], a problem closely related to the shuffling channel [16], [17], [28], [32]. This problem is motivated by DNA-based storage systems, where the information is stored in synthesized strands of DNA molecules.…”

Section: Introductionmentioning

confidence: 99%

Adversarial Torn-paper Codes

Bar-Lev¹,

Marcovich²,

Yaakobi³

et al. 2022

Preprint

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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 develop code constructions for any parameters of the channel for which non-vanishing asymptotic rate is possible and show 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.

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“…Notably, when observations are composed of consecutive substrings, the reconstruction from substring-compositions problem [1], [1], [4], [10], [12], [17], [19], [20], [25], [27], [31], [32] and the torn-paper problem [2], [21], [22], [28] (a problem closely related to the shuffling channel [11], [13], [26], [30]) have received significant interest in the past decade due to applications in DNA-or polymer-based storage systems, resulting from contemporary sequencing technologies [4], [9], [20]. The former arises from an idealized assumption of full overlap (and uniform coverage) in read substrings, while the latter results from an assumption of no overlap; in applications, this models the question of whether the complete information string may be replicated and uniformly segmented for sequencing, or if segmentation occurs adversarially in the medium prior to sequencing.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction from Substrings with Partial Overlap

Yehezkeally¹,

Bar-Lev²,

Marcovich³

et al. 2022

Preprint

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This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which all substrings of some fixed length are read or substrings are read with no overlap, this work considers the setup in which consecutive substrings are read with some given minimum overlap. First, upper bounds are provided on the attainable rates of codes that guarantee unique reconstruction. Then, we present efficient constructions of asymptotically optimal codes that meet the upper bound.

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The DNA Storage Channel: Capacity and Error Probability

Cited by 5 publications

References 34 publications

Information-Theoretic Foundations of DNA Data Storage

Information-Theoretic Foundations of DNA Data Storage

Adversarial Torn-paper Codes

Reconstruction from Substrings with Partial Overlap

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