Codes with Biochemical Constraints and Single Error Correction for DNA-Based Data Storage

TL;DR

This paper develops DNA codes that incorporate biochemical constraints and error correction to improve data storage reliability, achieving higher information rates and addressing secondary structure avoidance, homopolymer limits, and GC-balance.

Contribution

It introduces new DNA code constructions that satisfy multiple biochemical constraints and include single error correction, surpassing previous codes in rate and robustness.

Findings

Constructed DNA codes with secondary structure avoidance and homopolymer limits.

Achieved higher information rates, e.g., 1.3206 bits/nt for specific parameters.

Presented codes with GC-locally balanced constraints.

Abstract

In DNA-based data storage, DNA codes with biochemical constraints and error correction are designed to protect data reliability. Single-stranded DNA sequences with secondary structure avoidance (SSA) help to avoid undesirable secondary structures which may cause chemical inactivity. Homopolymer run-length limit and GC-balanced limit also help to reduce the error probability of DNA sequences during synthesizing and sequencing. In this letter, based on a recent work \cite{bib7}, we construct DNA codes free of secondary structures of stem length $\geq m$ and have homopolymer run-length $\leq\ell$ for odd $m\leq11$ and $\ell\geq3$ with rate $1+\log_2\rho_m-3/(2^{\ell-1}+\ell+1)$, where $\rho_m$ is in Table \ref{tm}. In particular, when $m=3$, $\ell=4$, its rate tends to 1.3206 bits/nt, beating a previous work by Benerjee {\it et al.}. We also construct DNA codes with all of the above three constraints as well as single error correction. At last, codes with GC-locally balanced constraint are presented.