DoDo-Code: an Efficient Levenshtein Distance Embedding-based Code for 4-ary IDS Channel

With the emergence of new storage and communication methods, the insertion, deletion, and substitution (IDS) channel has attracted considerable attention. However, many topics on the IDS channel and the associated Levenshtein distance remain open, making the invention of a novel IDS-correcting code a hard task. Furthermore, current studies on single-IDS-correcting code misalign with the requirements of applications which necessitates the correcting of multiple errors. Compromise solutions have involved shortening codewords to reduce the chance of multiple errors. However, the code rates of existing codes are poor at short lengths, diminishing the overall storage density. In this study, a novel method is introduced for designing high-code-rate single-IDS-correcting codewords through deep Levenshtein distance embedding. A deep learning model is utilized to project the sequences into embedding vectors that preserve the Levenshtein distances between the original sequences. This embedding space serves as a proxy for the complex Levenshtein domain, within which algorithms for codeword search and segment correcting is developed. While the concept underpinning this approach is straightforward, it bypasses the mathematical challenges typically encountered in code design. The proposed method results in a code rate that outperforms existing combinatorial solutions, particularly for designing short-length codewords.