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Coding for Strand Breaks in Composite DNA

Frederik Walter, Yonatan Yehezkeally

TL;DR

This work addresses the reliability of composite DNA data storage under strand-break errors by formalizing a composite symbol model with a base size $q$ and resolution $M$, yielding $Q=\binom{M+q-1}{q-1}$ composite symbols. It extends the strand-break channel to the composite setting and introduces a marker-based coding strategy coupled with a generalized composite Run-Length-Limited (RLL) framework, deriving both lower and upper bounds on redundancy and presenting a practical construction. A key contribution is a detailed redundancy analysis for composite RLL codes and a concrete code construction that inserts marker sequences to locate and reconstruct fragments, with an optimal marker length $\ell^{*}$ that minimizes redundancy (e.g., $\ell^{*} \approx \sqrt{(n-4)/2\cdot\log_Q(Q/(Q-R))}$). The proposed approach promises higher information density in DNA storage while maintaining reliability against single-break events, and it opens avenues for capacity analysis and extensions to more complex error models.

Abstract

Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the information capacity of each synthesis cycle and DNA storage systems in general by employing composite DNA symbols. Unlike conventional DNA storage, composite DNA encodes information in the distribution of bases across a pool of strands rather than in the individual strands themselves. Consequently, error models for DNA storage must be adapted to account for this unique characteristic. One significant error model for long-term DNA storage is strand breaks, often caused by the decay of individual bases. This work extends the strand-break channel model to the composite DNA setting. To address this challenge, we propose a coding scheme that uses marker codes to correct single strand breaks. As part of this approach, we generalise run-length-limited (RLL) codes for the composite setting and derive bounds on their redundancy.

Coding for Strand Breaks in Composite DNA

TL;DR

This work addresses the reliability of composite DNA data storage under strand-break errors by formalizing a composite symbol model with a base size and resolution , yielding composite symbols. It extends the strand-break channel to the composite setting and introduces a marker-based coding strategy coupled with a generalized composite Run-Length-Limited (RLL) framework, deriving both lower and upper bounds on redundancy and presenting a practical construction. A key contribution is a detailed redundancy analysis for composite RLL codes and a concrete code construction that inserts marker sequences to locate and reconstruct fragments, with an optimal marker length that minimizes redundancy (e.g., ). The proposed approach promises higher information density in DNA storage while maintaining reliability against single-break events, and it opens avenues for capacity analysis and extensions to more complex error models.

Abstract

Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the information capacity of each synthesis cycle and DNA storage systems in general by employing composite DNA symbols. Unlike conventional DNA storage, composite DNA encodes information in the distribution of bases across a pool of strands rather than in the individual strands themselves. Consequently, error models for DNA storage must be adapted to account for this unique characteristic. One significant error model for long-term DNA storage is strand breaks, often caused by the decay of individual bases. This work extends the strand-break channel model to the composite DNA setting. To address this challenge, we propose a coding scheme that uses marker codes to correct single strand breaks. As part of this approach, we generalise run-length-limited (RLL) codes for the composite setting and derive bounds on their redundancy.
Paper Structure (5 sections, 3 theorems, 29 equations, 2 figures)

This paper contains 5 sections, 3 theorems, 29 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions and Problem Statement
  3. Composite Run-Length-Limited Codes
  4. Code Construction
  5. Conclusion and Future Work

Key Result

Theorem 1

A lower bound on the redundancy of $\mathrm{RLL}_{Q,R}\left({\ell, n} \right)$ is given by

Figures (2)

  • Figure 1: Model for the composite strand break channel.
  • Figure 2: Example of a codeword with marker sequence and an RLL code

Theorems & Definitions (7)

  • Definition 1: Composite Symbol and Matrix
  • Definition 2: Composite RLL Code
  • Theorem 1
  • Theorem 2
  • Example 1
  • Corollary 1
  • Example 2