  Recently, DNA storage has surfaced as a promising alternative for data
storage, presenting notable benefits in terms of storage capacity,
cost-effectiveness in maintenance, and the capability for parallel replication.
Mathematically, the DNA storage process can be conceptualized as an insertion,
deletion, and substitution (IDS) channel. Due to the mathematical complexity
associated with the Levenshtein distance, creating a code that corrects for IDS
remains a challenging task. In this paper, we propose a bottom-up generation
approach to grow the required codebook based on the computation of Edit
Computational Graph (ECG) which differs from the algebraic constructions by
incorporating the Derivative-Free Optimization (DFO) method. Specifically, this
approach is regardless of the type of errors. Compared the results with the
work for 1-substitution-1-deletion and 2-deletion, the redundancy is reduced by
about 30-bit and 60-bit, respectively. As far as we know, our method is the
first IDS-correcting code designed using classical Natural Language Process
(NLP) techniques, marking a turning point in the field of error correction code
research. Based on the codebook generated by our method, there may be
significant breakthroughs in the complexity of encoding and decoding
algorithms.
