  Due to its longevity and enormous information density, DNA is an attractive
medium for archival data storage. 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.
