Fig. 1: Overview of the DNA StairLoop coding scheme.
a The error distribution of Yan et al.28, Antkowiak et al.9, and Nguyen et al.10. b Illustration of the encoding structure. The raw binary data are first divided into short sequences and then sequentially input into the blocks (in the positions of the raw information bits), forming a staircase layout. The raw information blocks subsequently undergo row encoding and column encoding to generate codewords, i.e., oligos. c Diagram of the decoding structure. The sequencing data first undergo raw decoding and are subsequently restored to the staircase blocks according to their indices. The row decoder is soft-input and soft-output, producing extrinsic information in the form of the log-likelihood ratio (LLR) of the raw information bits. The column decoder receives this extrinsic information and performs soft-decision column decoding, which outputs extrinsic information in the form of the LLR of the raw information bits as well. This extrinsic information is iteratively input back into the row decoder. The message passing path follows the red arrows shown in the diagram. The iteration between the row and column decoders continues until the stopping criterion is met, ultimately producing the decoded bits. d Trellis diagram of the row decoding scheme. The forward message, backward message, and current message are obtained from the trellis by tracing all possible trellis paths in the joint encoding state (ES) - drift state (DS) graph. The LLR of the i-th information bit is subsequently calculated based on the forward message, backward message, and current message in the i-th decoding moment. e Flowchart for parallel decoding. The stepped matrix is equally distributed among different nodes. Row and column decoding is performed within each node, and the first and last outer information matrix that is decoded is passed to the previous and next nodes. Source data are provided as a Source Data file.
