GC-balanced polar codes correcting insertions, deletions and substitutions for DNA storage

In order to address the insertion, deletion, and substitution (IDS) errors inherent in deoxyribonucleic acid (DNA) storage channels during DNA synthesis and sequencing, we propose a novel GC-balanced polar code scheme tailored to rectify these errors by incorporating the unique characteristics of the DNA storage channel into the polar code design. The innovation lies in modeling errors as a drift vector, reflecting deviations from the desired DNA sequence, aiming to improve the reliability of DNA-based data storage. In this paper, we developed a GC-balanced polar code scheme named DNA-BP Code, which stands for balanced polar code for DNA storage, that effectively rectifies IDS errors in DNA storage. The computational complexity of the proposed encoding and decoding algorithms is $\mathcal{O}(N\log N)$ with respect to the code length $N$. Simulation results show the bit error rate and block error rate as functions of the code length and IDS probability, demonstrating the efficacy of our approach in enhancing the accuracy of DNA storage systems.