Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Super-robust data storage in DNA by de Bruijn graph-based decoding

High density and long-term features make DNA data storage a potential media. However, DNA data channel is a unique channel with unavoidable ‘data reputations’ in the forms of multiple error-rich strand copies. This multi-copy feature cannot be well harnessed by available codec systems optimized for single-copy media. Furthermore, lacking an effective mechanism to handle base shift issues, these systems perform poorly with indels. Here, we report the efficient reconstruction of DNA strands from multiple error-rich sequences directly, utilizing a De Bruijn Graph-based Greedy Path Search (DBG-GPS) algorithm. DBG-GPS can take advantage of the multi-copy feature for efficient correction of indels as well as substitutions. As high as 10% of errors can be accurately corrected with a high coding rate of 96.8%. Accurate data recovery with low quality, deep error-prone PCR products proved the high robustness of DBG-GPS (314Kb, 12K oligos). Furthermore, DBG-GPS shows 50 times faster than the clustering and multiple alignment-based methods reported. The revealed linear decoding complexity makes DBG-GPS a suitable solution for large-scale data storage. DBG-GPS’s capacity with large data was verified by large-scale simulations (300 MB). A Python implementation of DBG-GPS is available at https://switch-codes.coding.net/public/switch-codes/DNA-Fountain-De-Bruijn-Decoding/git/files.