  We consider error-correcting coding for DNA-based storage. We model the DNA
storage channel as a multi-draw IDS 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
strands are prone to insertion, deletion, and substitution (IDS) errors. We
propose an index-based concatenated coding scheme consisting of the
concatenation of an outer code, an index code, and an inner synchronization
code, where the latter two tackle IDS errors. We further propose a mismatched
joint index-synchronization code maximum a posteriori probability decoder with
optional clustering to infer symbolwise a posterior probabilities for the outer
decoder. We compute achievable information rates for the outer code and present
Monte-Carlo simulations for information-outage probabilities and frame error
rates on synthetic and experimental data, respectively.
