The Synthesis-Sequencing Channel for DNA-based Data Storage

Jo\~ao Ribeiro; Keshav Goyal; Samuel Pearson; Serge Kas Hanna

arxiv: 2606.07216 · v1 · pith:HBT2NZPUnew · submitted 2026-06-05 · 💻 cs.IT · cs.ET· math.IT

The Synthesis-Sequencing Channel for DNA-based Data Storage

Keshav Goyal , Samuel Pearson , Jo\~ao Ribeiro , Serge Kas Hanna This is my paper

Pith reviewed 2026-06-27 20:38 UTC · model grok-4.3

classification 💻 cs.IT cs.ETmath.IT

keywords DNA-based data storagesynthesis-sequencing channelinformation-theoretic capacitybinary symmetric channelcoverage biasconverse boundachievability bound

0 comments

The pith

The synthesis-sequencing channel has an exact information-theoretic capacity given by matching converse and achievability bounds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the synthesis-sequencing channel as a two-stage model for DNA data storage that first applies synthesis to produce physical strands and then applies sequencing to produce reads. It derives matching upper and lower bounds on capacity when both stages are binary symmetric channels with possibly different error probabilities. The bounds hold under mild assumptions on the parameters and incorporate distinct physical coverage and sequencing coverage. This matters because the model captures coverage bias and relaxes independent-error assumptions that appeared in earlier work. The resulting capacity expression therefore quantifies the fundamental storage rate limit under the combined effects of synthesis errors, sequencing errors, and coverage depths.

Core claim

The synthesis-sequencing channel is formed by composing a synthesis stage followed by a sequencing stage. When synthesis and sequencing are each modeled by a binary symmetric channel, matching converse and achievability bounds establish the exact capacity under mild assumptions on the error probabilities and coverage parameters.

What carries the argument

The synthesis-sequencing channel, whose output statistics arise from the successive action of synthesis coverage, synthesis errors, sequencing coverage, and sequencing errors.

If this is right

The maximum reliable rate is determined by the product of synthesis coverage, sequencing coverage, and the two binary symmetric channel capacities adjusted for the induced bias.
Increasing physical coverage after synthesis trades off against increasing sequencing coverage in a manner that is not symmetric.
The model produces correlated errors across reads even when each individual stage is memoryless.
Exact capacity formulas become available for any parameter tuple obeying the mild conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Designers could allocate total sequencing effort between deeper synthesis and deeper readout to maximize the derived capacity.
The same two-stage composition idea could be applied to other storage media that undergo fabrication and readout stages.
Numerical evaluation of the capacity expression for concrete coverage and error values would immediately yield concrete rate targets for laboratory systems.

Load-bearing premise

The mild assumptions on the channel parameters that make the converse and achievability bounds coincide.

What would settle it

An explicit input distribution and decoding rule whose achieved rate exceeds the claimed capacity expression for any set of parameters satisfying the mild assumptions would falsify the result.

Figures

Figures reproduced from arXiv: 2606.07216 by Jo\~ao Ribeiro, Keshav Goyal, Samuel Pearson, Serge Kas Hanna.

**Figure 1.** Figure 1: Schematic illustration of the DNA synthesis–sequencing channel. Red symbols indicate synthesis errors that appear [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: Capacity (a) and coverage distributions (b) for the sequencing-only channel and several instances of the synthesis– [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

We introduce and study the synthesis-sequencing channel, a two-stage model for DNA-based data storage that jointly captures synthesis and sequencing effects. The synthesis-sequencing channel provides a more nuanced and realistic model of the DNA storage process compared to prior work, as it distinguishes between physical coverage after synthesis and sequencing coverage after readout, relaxes the assumption of independent errors across reads, and naturally induces coverage bias through the composition of synthesis and sequencing stages. We establish the information-theoretic capacity of this channel by deriving matching converse and achievability bounds for the case where synthesis and sequencing errors are modeled by binary symmetric channels with possibly different error probabilities, under mild assumptions on the channel parameters. Our results reveal multiple trade-offs between physical coverage, synthesis errors, sequencing coverage, and sequencing errors that influence the maximum achievable rate for reliable data storage.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines a joint synthesis-sequencing channel that distinguishes coverages and relaxes read independence, then claims matching capacity bounds for BSC errors under mild parameter assumptions whose scope remains unclear from the abstract.

read the letter

The main takeaway is a two-stage channel model for DNA storage that combines synthesis and sequencing, separates physical coverage from sequencing coverage, and lets composition create coverage bias while dropping the independent-reads assumption. That modeling choice is the clearest advance over earlier separate-stage treatments.

The paper does a clean job laying out the trade-offs among physical coverage, synthesis error rate, sequencing coverage, and sequencing error rate, and it states matching converse and achievability bounds when both stages are binary symmetric channels with possibly different crossover probabilities.

The soft spot is the explicit dependence on mild assumptions on the channel parameters for the bounds to coincide. The abstract does not spell out what those assumptions are, so it is not obvious whether the matching holds across the parameter ranges that matter in practice or only in narrower regimes. Without the derivations visible, it is also impossible to check for gaps in the steps that produce the bounds.

This is for information theorists who work on storage channels and DNA applications. A reader who wants to see how composite channels affect capacity calculations will get something concrete from the model itself.

I would send it to peer review so the assumptions and proofs can be examined directly.

Referee Report

1 major / 2 minor

Summary. The paper introduces the synthesis-sequencing channel, a two-stage model for DNA-based data storage that composes synthesis and sequencing stages, each modeled as a binary symmetric channel (BSC) with possibly distinct crossover probabilities. It distinguishes physical coverage after synthesis from sequencing coverage after readout, relaxes independent-error assumptions across reads, and induces coverage bias naturally. The central claim is that the information-theoretic capacity is established via matching converse and achievability bounds under mild assumptions on the channel parameters, with the results highlighting trade-offs among physical coverage, synthesis errors, sequencing coverage, and sequencing errors.

Significance. If the matching bounds hold under the stated assumptions, the work supplies the first capacity characterization for a more realistic DNA-storage channel that captures coverage bias and error dependence. This would be a substantive advance over prior models that treat synthesis and sequencing separately or assume uniform coverage, and the explicit trade-off analysis could inform practical parameter choices in DNA storage systems.

major comments (1)

[Abstract and capacity theorem statement] The abstract states that matching converse and achievability bounds are obtained 'under mild assumptions on the channel parameters,' yet the precise form of these assumptions (e.g., any inequalities relating the synthesis BSC crossover p, sequencing BSC crossover q, synthesis coverage, and sequencing coverage) is not visible in the provided text. Because the capacity result is explicitly conditioned on these assumptions, their necessity, scope, and practical relevance must be stated explicitly (ideally with a dedicated lemma or theorem statement) so that readers can determine whether the result applies to the general model or only to a restricted parameter region.

minor comments (2)

[Model definition] Notation for the two coverage parameters (physical vs. sequencing) should be introduced with a clear diagram or table early in the model section to avoid later ambiguity when discussing bias.
[Introduction] The abstract claims the model 'relaxes the assumption of independent errors across reads'; the manuscript should include a short paragraph contrasting the induced dependence structure with the independent-read models in prior work.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive suggestion. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Abstract and capacity theorem statement] The abstract states that matching converse and achievability bounds are obtained 'under mild assumptions on the channel parameters,' yet the precise form of these assumptions (e.g., any inequalities relating the synthesis BSC crossover p, sequencing BSC crossover q, synthesis coverage, and sequencing coverage) is not visible in the provided text. Because the capacity result is explicitly conditioned on these assumptions, their necessity, scope, and practical relevance must be stated explicitly (ideally with a dedicated lemma or theorem statement) so that readers can determine whether the result applies to the general model or only to a restricted parameter region.

Authors: We agree that the assumptions conditioning the capacity result should be stated explicitly and visibly. In the revised version we will add a dedicated Lemma 1 that lists all required conditions on p, q, synthesis coverage, and sequencing coverage (including any inequalities needed for the matching bounds), together with a short discussion of their necessity for the proof and their practical relevance. The abstract and the statement of the main capacity theorem will be updated to reference this lemma directly. revision: yes

Circularity Check

0 steps flagged

No circularity; standard capacity derivation with explicit assumptions.

full rationale

The paper derives matching converse and achievability bounds for the synthesis-sequencing channel (modeled via two BSCs) using standard information-theoretic techniques. The result is conditioned on explicitly stated mild assumptions on parameters, but no step reduces by construction to a fitted input, self-definition, or load-bearing self-citation chain. The central claim remains independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only review; ledger populated from explicitly stated elements. The model introduces a composite channel but relies on standard BSC assumptions and unspecified mild parameter conditions for the capacity result.

free parameters (2)

synthesis error probability
Parameter of the synthesis BSC stage; required for the capacity expression.
sequencing error probability
Parameter of the sequencing BSC stage; required for the capacity expression.

axioms (1)

domain assumption Mild assumptions on the channel parameters allow the converse and achievability bounds to match.
Explicitly invoked in the abstract as necessary for the capacity result.

pith-pipeline@v0.9.1-grok · 5673 in / 1247 out tokens · 33907 ms · 2026-06-27T20:38:38.518287+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 1 linked inside Pith

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Next-generation digital information storage in DNA,

G. M. Church, Y . Gao, and S. Kosuri, “Next-generation digital information storage in DNA,”Science, vol. 337, no. 6102, pp. 1628–1628, 2012

2012

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Robust chemical preservation of digital information on DNA in silica with error-correcting codes,

R. N. Grass, R. Heckel, M. Puddu, D. Paunescu, and W. J. Stark, “Robust chemical preservation of digital information on DNA in silica with error-correcting codes,”Angewandte Chemie International Edition, vol. 54, no. 8, pp. 2552–2555, 2015

2015

[3] [3]

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N. Goldman, P. Bertone, S. Chen, C. Dessimoz, E. M. LeProust, B. Sipos, and E. Birney, “Towards practical, high-capacity, low-maintenance information storage in synthesized DNA,”nature, vol. 494, no. 7435, pp. 77–80, 2013

2013

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S. H. T. Yazdi, R. Gabrys, and O. Milenkovic, “Portable and error-free DNA-based data storage,”Scientific reports, vol. 7, no. 1, p. 5011, 2017

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Improved read/write cost tradeoff in DNA-based data storage using LDPC codes,

S. Chandak, K. Tatwawadi, B. Lau, J. Mardia, M. Kubit, J. Neu, P. Griffin, M. Wootters, T. Weissman, and H. Ji, “Improved read/write cost tradeoff in DNA-based data storage using LDPC codes,” in2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2019, pp. 147–156

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Hedges error-correcting code for DNA storage corrects indels and allows sequence constraints,

W. H. Press, J. A. Hawkins, S. K. Jones Jr, J. M. Schaub, and I. J. Finkelstein, “Hedges error-correcting code for DNA storage corrects indels and allows sequence constraints,”Proceedings of the National Academy of Sciences, vol. 117, no. 31, pp. 18 489–18 496, 2020

2020

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DNA-Aeon provides flexible arithmetic coding for constraint adherence and error correction in DNA storage,

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2025

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DNA-MGC+: A versatile codec for reliable and resource-efficient data storage on synthetic DNA,

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2026

[10] [10]

A characterization of the DNA data storage channel,

R. Heckel, G. Mikutis, and R. N. Grass, “A characterization of the DNA data storage channel,”Scientific reports, vol. 9, no. 1, p. 9663, 2019

2019

[11] [11]

Information-theoretic foundations of DNA data storage,

I. Shomorony and R. Heckel, “Information-theoretic foundations of DNA data storage,”Foundations and Trends® in Communications and Information Theory, vol. 19, no. 1, pp. 1–106, 2022

2022

[12] [12]

Fundamental limits of DNA storage systems,

R. Heckel, I. Shomorony, K. Ramchandran, and D. N. Tse, “Fundamental limits of DNA storage systems,” in2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017, pp. 3130–3134

2017

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I. Shomorony and R. Heckel, “Capacity results for the noisy shuffling channel,” in2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019, pp. 762–766

2019

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DNA-based storage: Models and fundamental limits,

——, “DNA-based storage: Models and fundamental limits,”IEEE Transactions on Information Theory, vol. 67, no. 6, pp. 3675–3689, 2021

2021

[15] [15]

The DNA storage channel: Capacity and error probability bounds,

N. Weinberger and N. Merhav, “The DNA storage channel: Capacity and error probability bounds,”IEEE Transactions on Information Theory, vol. 68, no. 9, pp. 5657–5700, 2022

2022

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The noisy drawing channel: Reliable data storage in DNA sequences,

A. Lenz, P. H. Siegel, A. Wachter-Zeh, and E. Yaakobi, “The noisy drawing channel: Reliable data storage in DNA sequences,”IEEE Transactions on Information Theory, vol. 69, no. 5, pp. 2757–2778, 2023

2023

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DNA storage in the short molecule regime,

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arXiv 2025

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Concatenated codes for short-molecule DNA storage with sequencing channels of positive zero-undetected-error capacity,

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Pith/arXiv arXiv 2026

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N. Weinberger, “Error probability bounds for coded-index DNA storage systems,”IEEE Transactions on Information Theory, vol. 68, no. 11, pp. 7005–7022, 2022

2022

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Exact error exponents of concatenated codes for DNA storage,

Y . H. Ling and J. Scarlett, “Exact error exponents of concatenated codes for DNA storage,”IEEE Transactions on Information Theory, vol. 71, no. 9, pp. 6566–6585, 2025

2025

[21] [21]

Error exponents for DNA storage codes with a variable number of reads,

Y . H. Ling, N. Weinberger, and J. Scarlett, “Error exponents for DNA storage codes with a variable number of reads,” IEEE Journal on Selected Areas in Information Theory, vol. 6, pp. 205–216, 2025

2025

[22] [22]

Low cost DNA data storage using photolithographic synthesis and advanced information reconstruction and error correction,

P. L. Antkowiak, J. Lietard, M. Z. Darestani, M. M. Somoza, W. J. Stark, R. Heckel, and R. N. Grass, “Low cost DNA data storage using photolithographic synthesis and advanced information reconstruction and error correction,”Nature communications, vol. 11, no. 1, p. 5345, 2020

2020

[23] [23]

Comparison of state-of-the-art error-correction coding for sequence-based DNA data storage,

A. L. Gimpel, A. Remschak, W. J. Stark, R. Heckel, and R. N. Grass, “Comparison of state-of-the-art error-correction coding for sequence-based DNA data storage,”Nature Communications, 2026

2026

[24] [24]

A digital twin for DNA data storage based on comprehensive quantification of errors and biases,

A. L. Gimpel, W. J. Stark, R. Heckel, and R. N. Grass, “A digital twin for DNA data storage based on comprehensive quantification of errors and biases,”Nature Communications, vol. 14, no. 1, p. 6026, 2023

2023

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T. M. Cover and J. A. Thomas,Elements of Information Theory 2nd Edition (Wiley Series in Telecommunications and Signal Processing). Wiley-Interscience, July 2006

2006

[26] [26]

A mathematical theory of communication,

C. E. Shannon, “A mathematical theory of communication,”The Bell System Technical Journal, vol. 27, pp. 379–423,

[27] [27]

Available: http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf

[Online]. Available: http://plan9.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf