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Error-correcting codes (ECCs) employed in the state-of-the-art DNA digital storage (DDS) systems suffer from a trade-off between error-correcting capability and the proportion of redundancy. To address this issue, in this study, we introduce soft-decision decoding approach into DDS by proposing a DNA-specific error prediction model and a series of novel strategies. We demonstrate the effectiveness of our approach through a proof-of-concept DDS system based on Reed-Solomon (RS) code, named as Derrick. Derrick shows significant improvement in error-correcting capability without involving additional redundancy in both in vitro and in silico experiments, using various sequencing technologies such as Illumina, PacBio and Oxford Nanopore Technology (ONT). Notably, in vitro experiments using ONT sequencing at a depth of 7× reveal that Derrick, compared with the traditional hard-decision decoding strategy, doubles the error-correcting capability of RS code, decreases the proportion of matrices with decoding-failure by 229-fold, and amplifies the potential maximum storage volume by impressive 32 388-fold. Also, Derrick surpasses 'state-of-the-art' DDS systems by comprehensively considering the information density and the minimum sequencing depth required for complete information recovery. Crucially, the soft-decision decoding strategy and key steps of Derrick are generalizable to other ECCs' decoding algorithms. [ABSTRACT FROM AUTHOR]