  Decoding sequences that stem from multiple transmissions of a codeword over
an insertion, deletion, and substitution channel is a critical component of
efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we
consider a concatenated coding scheme with an outer low-density parity-check
code and either an inner convolutional code or a block code. We propose two new
decoding algorithms for inference from multiple received sequences, both
combining the inner code and channel to a joint hidden Markov model to infer
symbolwise a posteriori probabilities (APPs). The first decoder computes the
exact APPs by jointly decoding the received sequences, whereas the second
decoder approximates the APPs by combining the results of separately decoded
received sequences. Using the proposed algorithms, we evaluate the performance
of decoding multiple received sequences by means of achievable information
rates and Monte-Carlo simulations. We show significant performance gains
compared to a single received sequence.
