Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

Abstract

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 paritycheck 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.

Trellis BMA: Coded Trace Reconstruction on IDS Channels for DNA Storage

“…• A low-complexity heuristic dubbed Trellis BMA is proposed that allows multiple single-trace trellis decoders to interact and estimate the input message on-the-fly. This is different from the approaches in [23], [27], [28] because each singletrace trellis decoder is influenced by the other decoders but it is related to the factor graph method in [22]. Our idea marries BCJR inference [20] for IDS channels [21] with the consensus approach of BMA, hence the name Trellis BMA.…”

“…Thus, an outer code is required and sequence numbers must be included for disambiguation [30]. This detail is sometimes neglected in simulation-based experiments (e.g., it seems a single long strand is used in [23]).…”

“…In particular, we target schemes where the inner codes are decoded first followed by the outer code. In contrast to [23], we do not consider iteration between the inner and outer decoder nor do we estimate the error rate after decoding of the outer code.…”

“…Thus, we focus primarily on approximate reconstruction, as opposed to exact reconstruction. For IDS-like channels, one can compute exact posterior marginals by combining ideas from multiplesequence alignment [10] and the BCJR algorithm [20] (e.g., see [21]- [23]). Using these posterior marginals, it is easy to compute estimates that minimize additive distortion measures.…”

“…The inner code constraints can also be included in channel trellis [26] so that trellis-based methods can still be used for inference. In particular, for convolutional codes, it is possible to build a multidimensional trellis and perform symbolwise maximuma-posteriori (MAP) reconstruction, as observed in [23]. But, the complexity grows exponentially with the number of traces making exact inference infeasible.…”