Constrained Coding for Composite DNA: Channel Capacity and Efficient Constructions

TL;DR

This paper develops constrained coding techniques for composite DNA data storage, enhancing capacity and reliability by enforcing biological constraints and designing efficient encoding schemes.

Contribution

It introduces capacity analysis and construction of capacity-approaching codes for composite DNA, addressing sequencing errors and biological constraints.

Findings

Capacity of constrained composite DNA channel computed

Efficient encoders/decoders designed with minimal redundancy

Achieved near-capacity coding with only one redundant symbol for some parameters

Abstract

Composite DNA is a recent novel method to increase the information capacity of DNA-based data storage above the theoretical limit of 2 bits/symbol. In this method, every composite symbol does not store a single DNA nucleotide but a mixture of the four nucleotides in a predetermined ratio. By using different mixtures and ratios, the alphabet can be extended to have much more than four symbols in the naive approach. While this method enables higher data content per synthesis cycle, potentially reducing the DNA synthesis cost, it also imposes significant challenges for accurate DNA sequencing since the base-level errors can easily change the mixture of bases and their ratio, resulting in changes to the composite symbols. With this motivation, we propose efficient constrained coding techniques to enforce the biological constraints, including the runlength-limited constraint and the GC-content constraint, into every DNA synthesized oligo, regardless of the mixture of bases in each composite letter and their corresponding ratio. Our goals include computing the capacity of the constrained channel, constructing efficient encoders/decoders, and providing the best options for the composite letters to obtain capacity-approaching codes. For certain codes' parameters, our methods incur only one redundant symbol.