Coding for Optimized Writing Rate in DNA Storage

Jain, Siddharth; Farnoud, Farzad; Schwartz, Moshe; Bruck, Jehoshua

doi:10.1109/isit44484.2020.9174253

Cited by 26 publications

(11 citation statements)

References 17 publications

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“…In many applications it helpful for the synthesized strands to fulfill certain constraints, such as forbidding specified substrings [MRRY21,JFSB20]. We thus present a method to compute the maximum synthesis information rate under a constraint.…”

Section: Constrained Synthesismentioning

confidence: 99%

Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

Lenz¹,

Melczer²,

Rashtchian³

et al. 2021

Preprint

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Analytic combinatorics in several variables is a powerful tool for deriving the asymptotic behavior of combinatorial quantities by analyzing multivariate generating functions. We study information-theoretic questions about sequences in a discrete noiseless channel under cost and forbidden substring constraints. Our main contributions involve the relationship between the graph structure of the channel and the singularities of the bivariate generating function whose coefficients are the number of sequences satisfying the constraints. We combine these new results with methods from multivariate analytic combinatorics to solve questions in many application areas. For example, we determine the optimal coded synthesis rate for DNA data storage when the synthesis supersequence is any periodic string. This follows from a precise characterization of the number of subsequences of an arbitrary periodic strings. Along the way, we provide a new proof of the equivalence of the combinatorial and probabilistic definitions of the costconstrained capacity, and we show that the cost-constrained channel capacity is determined by a cost-dependent singularity, generalizing Shannon's classical result for unconstrained capacity.

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Section: Constrained Synthesismentioning

confidence: 99%

Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

Lenz¹,

Melczer²,

Rashtchian³

et al. 2021

Preprint

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“…In this section, we introduce another degree of freedom into our setting, which is the decoder's ability to return a list of codewords instead of a single one. We show that by doing so, the decoder requires substantially fewer vectors from the channel, compared with (9). We shall modify the reconstruction algorithms in Section V to produce a list of candidates L which contains the transmitted codeword x.…”

Section: List Decoding With Multiple Received Sequencesmentioning

confidence: 99%

“…This paper focuses on limited-magnitude errors, which could be found in several applications, including highdensity magnetic recording channels [13], [16], flash memories [4], and some DNA-based storage systems [9], [25].…”

Section: Introductionmentioning

confidence: 99%

Sequence Reconstruction for Limited-Magnitude Errors

Wei¹,

Schwartz²

2021

Preprint

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Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in relation to the code's minimum distance. We also devise efficient reconstruction algorithms for various limitedmagnitude error parameter ranges. We then extend these algorithms to the list-reconstruction scheme, and show the trade-off between the asymptotic list size and the number of required channel outputs. These results apply to all codes, without any assumptions on the code structure. Finally, we also study linear reconstruction codes with small intersection, as well as show a connection to list-reconstruction codes for the tandem-duplication channel.

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“…Lenz et al study reference strings that have a large number of subsequences, and they consider mappings to encode data by a set of strings while minimizing the single-batch synthesis cost [30]. A slightly different synthesis model has also been considered, where information is stored based on run-length patterns in the strings [1,29,21].…”

Section: Related Workmentioning

confidence: 99%

Batch Optimization for DNA Synthesis

Makarychev¹,

Rácz²,

Rashtchian³

et al. 2020

Preprint

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Large pools of synthetic DNA molecules have been recently used to reliably store significant volumes of digital data. While DNA as a storage medium has enormous potential because of its high storage density, its practical use is currently severely limited because of the high cost and low throughput of available DNA synthesis technologies.We study the role of batch optimization in reducing the cost of large scale DNA synthesis, which translates to the following algorithmic task. Given a large pool S of random quaternary strings of fixed length, partition S into batches in a way that minimizes the sum of the lengths of the shortest common supersequences across batches.We introduce two ideas for batch optimization that both improve (in different ways) upon a naive baseline: (1) using both (ACGT ) * and its reverse (T GCA) * as reference strands, and batching appropriately, and (2) batching via the quantiles of an appropriate ordering of the strands. We also prove asymptotically matching lower bounds on the cost of DNA synthesis, showing that one cannot improve upon these two ideas. Our results uncover a surprising separation between two cases that naturally arise in the context of DNA data storage: the asymptotic cost savings of batch optimization are significantly greater in the case where strings in S do not contain repeats of the same character (homopolymers), as compared to the case where strings in S are unconstrained.

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Coding for Optimized Writing Rate in DNA Storage

Cited by 26 publications

References 17 publications

Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

Multivariate Analytic Combinatorics for Cost Constrained Channels and Subsequence Enumeration

Sequence Reconstruction for Limited-Magnitude Errors

Batch Optimization for DNA Synthesis

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