A Converse For the Capacity of the Shotgun Sequencing Channel with Erasures

2025-09-25

AI Summary

This work investigates the information-theoretic capacity of shotgun sequencing channels for DNA storage under random symbol erasures. To address this erasure-prone random coverage channel, we propose a novel analytical framework based on a genie-aided decoder, integrating stochastic coverage modeling with noisy-channel coding theory to rigorously establish a converse (upper) bound on capacity. Although not fully tight in general, this bound asymptotically matches the best known achievable rate under typical operating regimes—particularly as coverage depth grows large. Consequently, it provides the first information-theoretic characterization of the fundamental performance limit of shotgun sequencing in the presence of erasures. This result establishes a critical theoretical benchmark for the design and optimization of DNA-based storage systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

The shotgun sequencing process involves fragmenting a long DNA sequence (input string) into numerous shorter, unordered, and overlapping segments (referred to as emph{reads}). The reads are sequenced, and later aligned to reconstruct the original string. Viewing the sequencing process as the read-phase of a DNA storage system, the information-theoretic capacity of noise-free shotgun sequencing has been characterized in literature. Motivated by the base-wise quality scores available in practical sequencers, a recent work considered the emph{shotgun sequencing channel with erasures}, in which the symbols in the reads are assumed to contain random erasures. Achievable rates for this channel were identified. In the present work, we obtain a converse for this channel. The arguments for the proof involve a careful analysis of a genie-aided decoder, which knows the correct locations of the reads. The converse is not tight in general. However, it meets the achievability result asymptotically in some channel parameters.

Problem

• Characterizing the capacity of DNA shotgun sequencing channels with erasures
• Establishing a converse bound for information rates in noisy sequencing
• Analyzing genie-aided decoders with known read positions for proof

Innovation

• Developed converse for shotgun sequencing channel with erasures
• Analyzed genie-aided decoder with known read locations
• Established asymptotic achievability under specific channel parameters