Figure 1.

Schematic diagram of Derrick decoding algorithm and soft-decision decoding strategy with sequence composition of synthesized DNA molecules. (A) The Pipeline of Derrick decoding algorithm. The left panel provides a literary description of the steps of Derrick algorithm, while the right panel depicts the consensus building, error prediction, soft-decision strategy and shifting steps. Initially, the consensus sequence is generated from the aligned reads and the confidence score of each nucleotide is calculated. Subsequently, the consensus sequence is cut and reassembled into matrices where the yellow frame on the matrix represents an RS block and different colors of the matrix indicate different confidence scores. For each block, the algorithm first tries the hard-decision decoding approach. If this fails, it employs the soft-decision decoding strategy, selecting the positions with the lowest confidence scores as potential error positions and adding them to the prediction set. The prediction set is then used for iterative soft-decision decoding until the block is successfully corrected. After each block is decoded, the algorithm adjusts the erroneous subsequences in the matrix based on the realignments between the original and corrected sequences to reduce errors in subsequent blocks. (B) Schematic diagram of RS soft-decision decoding strategy. Three RS codes, a, b₁ and b₂, are to be decoded (corrected). A and B are two candidate solutions that the RS codes (a, b₁ and b₂) may be decoded (corrected) into. The blue and orange circles represent the error-correcting capability of the hard-decision strategy for A and B. In Derrick, since a is within the decoding capability of A (inside blue circle), it is corrected into A by hard-decision strategy. For b₁, Derrick carries out soft-decision decoding by gradually increasing the black circle representing iteratively searching larger subsets of the prediction set until it (the second black circle) reaches the capability (orange circle) of B and is corrected into B. Similarly, b₂ is corrected into A by the soft-decision strategy in Derrick after reaching the capability (blue circle) of A. Although A is the closest solution to b₂, the correct solution is B (the second closest solution). Therefore, CRC64 shows the mistake, and the algorithm backtracks and recorrects b₂ to B by continuing to search larger subsets of the prediction set (increasing black circle) until it reaches the capability (orange circle) of B to correct b2 into B. (C) Sequence composition of each synthesized DNA molecule, where ‘nt’ represents nucleotides.