Information-Theoretic Foundations of DNA Data Storage

Abstract

Due to its longevity and enormous information density, DNA is an attractive medium for archival data storage. Natural DNA more than 700.000 years old has been recovered, and about 5 grams of DNA can in principle hold a Zetabyte of digital information, orders of magnitude more than what is achieved on conventional storage media. Thanks to rapid technological advances, DNA storage is becoming practically feasible, as demonstrated by a number of experimental storage systems, making it a promising solution for our society's increasing need of data storage.While in living things, DNA molecules can consist of millions of nucleotides, due to technological constraints, in practice, data is stored on many short DNA molecules, which are preserved in a DNA pool and cannot be spatially ordered. Moreover, imperfections in sequencing, synthesis, and handling, as well as DNA decay during storage, introduce random noise into the system, making the task of reliably storing and retrieving information in DNA challenging.This unique setup raises a natural information-theoretic question: how much information can be reliably stored on and reconstructed from millions of short noisy sequences? The goal of this monograph is to address this question by discussing the fundamental limits of storing information on DNA. Motivated by current technological constraints on DNA synthesis and sequencing, we propose a probabilistic channel model that captures three key distinctive aspects of the DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered fashion; (2) the molecules are corrupted by noise and (3) the data is read by randomly sampling from the DNA pool. Our goal is to investigate the impact of each of these key aspects on the capacity of the DNA storage system. Rather than focusing on coding-theoretic considerations and computationally efficient encoding and decoding, we aim to build an information-theoretic foundation for the analysis of these channels, developing tools for achievability and converse arguments.

Emerging Approaches to DNA Data Storage: Challenges and Prospects

“…However, it cannot correct large error rates that are dominated by insertions and deletions. This is because no inner codes exist that work sufficiently well on short sequences in these noisy setups . Here, the original message can be recovered by additionally exploiting the physical redundancy.…”

“…This is because no inner codes exist that work sufficiently well on short sequences in these noisy setups. 92 Here, the original message can be recovered by additionally exploiting the physical redundancy. For example, in Antkowiak et al, 42 the noisy sequences were first clustered by similarity, then the information on multiple erroneous copies was combined to construct a sequence with fewer errors.…”

Sequencing coverage analysis for combinatorial DNA-based storage systems

“…While DNA-based storage stands as a promising technology, and the cost of DNA sequencing has been decreasing, it remains significantly more expensive than reading from established archival storage solutions [9] [10] [11] [12]. In the context of DNA sequencing costs and throughput, recent work [13] defined the DNA coverage depth problem, which considers the expected sample size, to guarantee successful decoding of the information.…”

Robust Indexing - Optimal Codes for DNA Storage

“…Other related problem settings include: permutation channels [15], [16], [21], [28], [33], which consider string errors only, and torn paper coding [3], [25]. See [24] for a broader survey of the related problems.…”