The DNA Storage Channel: Capacity and Error Probability

TL;DR

This paper analyzes the capacity and error probability of DNA storage channels, providing bounds that generalize previous results and relax restrictions, especially in high-noise scenarios, with implications for reliable data retrieval.

Contribution

It introduces generalized bounds on DNA storage channel capacity and reliability, extending previous models to more realistic conditions and high-noise regimes.

Findings

Bounds on capacity are established for various noise levels.

Lower bounds on reliability function are achieved with a universal decoder.

Restrictions on molecule length scaling are relaxed in high-noise conditions.

Abstract

The DNA storage channel is considered, in which the $M$ Deoxyribonucleic acid (DNA) molecules comprising each codeword are stored without order, sampled $N$ times with replacement, and then sequenced over a discrete memoryless channel. For a constant coverage depth $M/N$ and molecule length scaling $\Theta(\log M)$, lower (achievability) and upper (converse) bounds on the capacity of the channel, as well as a lower (achievability) bound on the reliability function of the channel are provided. Both the lower and upper bounds on the capacity generalize a bound which was previously known to hold only for the binary symmetric sequencing channel, and only under certain restrictions on the molecule length scaling and the crossover probability parameters. When specified to binary symmetric sequencing channel, these restrictions are completely removed for the lower bound and are significantly relaxed for the upper bound in the high-noise regime. The lower bound on the reliability function is achieved under a universal decoder, and reveals that the dominant error event is that of outage -- the event in which the capacity of the channel induced by the DNA molecule sampling operation does not support the target rate.