Symbolwise MAP for Multiple Deletion Channels

Srinivasavaradhan, Sundara Rajan; Du, Michelle; Diggavi, Suhas; Fragouli, Christina

doi:10.1109/isit.2019.8849567

Cited by 14 publications

(7 citation statements)

References 15 publications

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“…• 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.…”

Section: A Contributionsmentioning

confidence: 98%

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

Srinivasavaradhan¹,

Gopi²,

Pfister³

et al. 2021

Preprint

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Sequencing a DNA strand, as part of the read process in DNA storage, produces multiple noisy copies which can be combined to produce better estimates of the original strand; this is called trace reconstruction. One can reduce the error rate further by introducing redundancy in the write sequence and this is called coded trace reconstruction. In this paper, we model the DNA storage channel as an insertion-deletion-substitution (IDS) channel and design both encoding schemes and low-complexity decoding algorithms for coded trace reconstruction.We introduce Trellis BMA, a new reconstruction algorithm whose complexity is linear in the number of traces, and compare its performance to previous algorithms. Our results show that it reduces the error rate on both simulated and experimental data. The performance comparisons in this paper are based on a new dataset of traces that will be publicly released with the paper. Our hope is that this dataset will enable research progress by allowing objective comparisons between candidate algorithms.

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Section: A Contributionsmentioning

confidence: 98%

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

Srinivasavaradhan¹,

Gopi²,

Pfister³

et al. 2021

Preprint

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“…In our simulations we used this improvement when implementing the ML D decoder. Other improvements and algorithms of the ML decoder are discussed in [76], [77].…”

Section: Two Deletion Channelsmentioning

confidence: 99%

On The Decoding Error Weight of One or Two Deletion Channels

Sabary¹,

Bar-Lev²,

Gershon³

et al. 2022

Preprint

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This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm, a word is transmitted over some fixed number of identical independent channels and the goal of the decoder is to output the transmitted word or some close approximation of it. The first part of this paper studies the deletion channel that deletes a symbol with some fixed probability p, while focusing on two instances of this channel. Since operating the maximum likelihood (ML) decoder in this case is computationally unfeasible, we study a slightly degraded version of this decoder for two channels and study its expected normalized distance. We observe that the dominant error patterns are deletions in the same run or errors resulting from alternating sequences. Based on these observations, it is derived that the expected normalized distance of the degraded ML decoder is roughly 3q−1 q−1 p 2 , when the transmitted word is any q-ary sequence and p is the channel's deletion probability. We also study the cases when the transmitted word belongs to the Varshamov Tenengolts (VT) code or the shifted VT code. Additionally, the insertion channel is studied as well as the case of two insertion channels. These theoretical results are verified by corresponding simulations. The second part of the paper studies optimal decoding for a special case of the deletion channel, referred by the k-deletion channel, which deletes exactly k symbols of the transmitted word uniformly at random. In this part, the goal is to understand how an optimal decoder operates in order to minimize the expected normalized distance. A full characterization of an efficient optimal decoder for this setup, reffered to as the maximum likelihood* (ML*) decoder, is given for a channel that deletes one or two symbols. For k = 1 it is shown that when the code is the entire space, the decoder is the lazy decoder which simply returns the channel output. Similarly, for k = 2 it is shown that the decoder acts as the lazy decoder in almost all cases and when the longest run is significantly long (roughly (2 − √ 2)n when n is the word length), it prolongs the longest run by one symbol.

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“…While these works mainly derive asymptotic results, here we discuss a fixed number of short, finite-length received sequences over a channel that additionally allows insertions and substitutions. More recently, the trace reconstruction problem has also been formulated for a fixed number of sequences with a larger focus on algorithmic aspects [15], [16]. However, these works consider only uncoded sequences, while we are interested in the case of coded transmission.…”

Section: Introductionmentioning

confidence: 99%

Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

Lenz

Maarouf

Welter

et al. 2021

2020 IEEE Information Theory Workshop (ITW)

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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.

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Symbolwise MAP for Multiple Deletion Channels

Cited by 14 publications

References 15 publications

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

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

On The Decoding Error Weight of One or Two Deletion Channels

Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

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