An End-to-End Coding Scheme for DNA-Based Data Storage With Nanopore-Sequenced Reads

TL;DR

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.

Abstract

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.%

Figures (13)

• Figure 1: Adapted state-based memory-$k$ nanopore ($\textsf{KMER}_k$) channel inspired from frenchKmer_belaid_2023. We have $k\text{mer}_t = (x_{t-\lfloor{\frac{k}{2}}\rfloor}, \dots, x_t, \dots, x_{t+\lfloor{\frac{k}{2}}\rfloor})$ and abbreviate $p_{\tt{{Ins}}} = p({\tt{{Ins}}} | k\text{mer}_t , e)$, $p_{\tt{{Del}}} = p({\tt{{Del}}} | k\text{mer}_t , e)$, $p_{\tt{{Sub}}} = p({\tt{{Sub}}} | k\text{mer}_t , e)$, and $p_{\tt{Tra}} = p({\tt{Tra}} | k\text{mer}_t , e)$.
• Figure 2: Sampling KMER channel model. First, each input strand gets copied randomly. Second, the strands get reverse-complemented (RC) according to a Bernoulli RV and get consequently labeled as forward or backward reads (see $(\cdot)^\mathrm{f}$/$(\cdot)^\mathrm{b}$). Third, the resulting strands are passed through independent $\textsf{KMER}_k^\mathrm{f}$/$\textsf{KMER}_k^\mathrm{b}$ channels. Fourth, the strands are randomly permuted.
• Figure 3: Concatenated coding scheme for communication over the multi-draw KMER channel. For each block ${\boldsymbol w}^{(i)}$, the corresponding index vector is split into two parts and inserted at the beginning and the end of the block together with the primers ${\boldsymbol p}_1$ and ${\boldsymbol p}_2$. Joint-code refers to the combination of primer, index, and inner code. We use ${\cal C}_\mathrm{ix}(\cdot)$ and ${\cal C}_\mathrm{i}(\cdot)$ as the encoding functions for the index code and inner code, respectively. The reads ${\boldsymbol y}_1,\ldots, {\boldsymbol y}_N$ are either labeled forward or backward reads. The term $q(w_t|{\boldsymbol Y})$ denotes the mismatched symbol APPs computed by the joint-code decoder. Further, the symbols $\Pi$ and $\Pi^{-1}$ represent the random interleaving and its reversal operation, respectively.
• Figure 4: Simplified decoding flow (no outer decoding). For simplicity, we do not differentiate forward or backward reads. The arrows in the last row of the figure indicate the resulting assignments of the DNA reads ${\boldsymbol y}_1,\ldots,{\boldsymbol y}_6$ to the respective outer codeword blocks.
• Figure 5: Read/write cost trade-off for our setup and other experiments. Some experiments conducted storage trials with various parameters. We have selected the one that appears to be the best based on our knowledge. Label references: Lau-2023stanford_magneticDNAstorage_2023, Bar-Lev-2021bar2021deep, Antkowiak-2020antkowiak_low_2020, Chandak-2020chandak_overcoming_2020, Anavy-2019Anavy2019composite, Chandak-2019chandak_improved_2019, Lopez-2019Lopez2019, Organick-2019organick_random_2018, Erlich-2017erlich_dna_2017, Yazdi-2017yazdi_portable_2017, and Bornholt-2016bornholt_dna-based_2016.