Concatenated Codes for Short-Molecule DNA Storage with Sequencing Channels of Positive Zero-Undetected-Error Capacity

2026-02-13

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

We study the amount of reliable information that can be stored in a DNA-based storage system with noisy sequencing, where each codeword is composed of short DNA molecules. We analyze a concatenated coding scheme, where the outer code is designed to handle the random sampling, while the inner code is designed to handle the random sequencing noise. We assume that the sequencing channel is symmetric and choose the inner coding scheme to be composed by a linear block code and a zero-undetected-error decoder. As a byproduct, the resulting optimal maximum-likelihood decoder land itself for an amenable analysis, and we are able to derive an achievability bound for the scaling of the number of information bits that can be reliably stored. As a result of independent interest, we prove that the average error probability of random linear block codes under zero-undetected-error decoding converges to zero exponentially fast with the block length, as long as its coding rate does not exceed some critical value, which is known to serve as a lower bound to the zero-undetected-error capacity.

Problem

• DNA storage
• sequencing noise
• concatenated codes
• zero-undetected-error capacity
• short-molecule

Innovation

• concatenated coding
• DNA storage
• zero-undetected-error decoding
• linear block codes
• achievable information scaling