  We consider error-correcting coding for deoxyribonucleic acid (DNA)-based
storage using nanopore sequencing. We model the DNA storage channel as a
sampling noise channel where the input data is chunked into $M$ short DNA
strands, which are copied a random number of times, and the channel outputs a
random selection of $N$ noisy DNA strands. The retrieved DNA reads are prone to
strand-dependent insertion, deletion, and substitution (IDS) errors. We
construct an index-based concatenated coding scheme consisting of the
concatenation of an outer code, an index code, and an inner code. We further
propose a low-complexity (linear in $N$) maximum a posteriori probability
decoder that takes into account the strand-dependent IDS errors and the
randomness of the drawing to infer symbolwise a posteriori probabilities for
the outer decoder. We present Monte-Carlo simulations for information-outage
probabilities and frame error rates for different channel setups on
experimental data. We finally evaluate the overall system performance using the
read/write cost trade-off. A powerful combination of tailored channel modeling
and soft information processing allows us to achieve excellent performance even
with error-prone nanopore-sequenced reads outperforming state-of-the-art
schemes.%
