Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

TL;DR

This paper analyzes the limits of concatenated coding schemes for DNA storage channels with substitution errors, revealing a gap from capacity and proposing a modified scheme to improve achievable rates.

Contribution

It identifies the gap between achievable rates of standard concatenated codes and channel capacity in DNA storage, and introduces a modified coding scheme to close this gap.

Findings

Standard concatenated codes underperform relative to capacity in DNA storage.

Combining multiple strands into one inner block improves achievable rates.

Modified coding scheme narrows the gap to channel capacity.

Abstract

In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each strand is replicated many times. Third, the data is accessed in an uncontrollable manner, i.e., random strands are drawn from the medium and received, possibly with errors. As one of our results, we show that there is a significant gap between the channel capacity and the achievable rate of a standard concatenated code in which one strand corresponds to an inner block. This is in fact surprising as for other channels, such as $q$-ary symmetric channels, concatenated codes are known to achieve the capacity. We further propose a modified concatenated coding scheme by combining several strands into one inner block, which allows to narrow the gap and achieve rates that are close to the capacity.