On Coding Over Sliced Information

Sima, Jin; Raviv, Netanel; Bruck, Jehoshua

doi:10.1109/isit.2019.8849596

Cited by 21 publications

(20 citation statements)

References 21 publications

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“…In [13], unordered multisets with errors that affect the whole sequence have been discussed. Furthermore, the model proposed in this work has already been adopted in [14], [15]. Namely, codes and bounds for an arbitrary number of substitutions in sets of DNA strands have been derived in [14] and it has been shown that it is possible to construct codes, which have logarithmic redundancy on both, the number of sequences and the length of the sequences.…”

Section: Introductionmentioning

confidence: 99%

Coding Over Sets for DNA Storage

Lenz

Siegel

Wachter-Zeh

et al. 2020

IEEE Trans. Inform. Theory

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In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of M sequences, each of length L. Errors within that model are a loss of whole sequences and point errors inside the sequences, such as insertions, deletions and substitutions. We derive Gilbert-Varshamov lower bounds and sphere packing upper bounds on achievable cardinalities of error-correcting codes within this storage model. We further propose explicit code constructions than can correct errors in such a storage system that can be encoded and decoded efficiently. Comparing the sizes of these codes to the upper bounds, we show that many of the constructions are close to optimal.Index Terms-coding over sets, DNA data storage, Gilbert-Varshamov bound, insertion and deletion errors, sphere packing bound

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Section: Introductionmentioning

confidence: 99%

Coding Over Sets for DNA Storage

Lenz

Siegel

Wachter-Zeh

et al. 2020

IEEE Trans. Inform. Theory

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“…Some recent works have focused on coding for other channel models inspired by DNA-based storage. The model studied in [27,28,29,30] views codewords as sets comprised of several sequences over some alphabet, and the (adversarial) errors consist of erasure and insertion of sequences in the set, as well as deletions, insertions, or substitutions within some of the sequences. Each sequence in the set corresponds to a different DNA strand whose contents are reconstructed via high throughput sequencing-based procedures that introduce errors.…”

Section: Introductionmentioning

confidence: 99%

Coded Trace Reconstruction

Cheraghchi

Ribeiro

Gabrys

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads (also called traces) corrupted by edit errors. Codes used in current portable DNA-based storage systems with nanopore sequencers are largely based on heuristics, and have no provable robustness or performance guarantees even for an error model with i.i.d. deletions and constant deletion probability. Our work is a first step towards the design of efficient codes with provable guarantees for such systems. We consider a constant rate of i.i.d. deletions, and perform an analysis of marker-based code-constructions. This gives rise to codes with redundancy O(n/ log n) (resp. O(n/ log log n)) that can be efficiently reconstructed from exp(O(log 2/3 n)) (resp. exp(O(log log n) 2/3 )) traces, where n is the message length. Then, we give a construction of a code with O(log n) bits of redundancy that can be efficiently reconstructed from poly(n) traces if the deletion probability is small enough. Finally, we show how to combine both approaches, giving rise to an efficient code with O(n/ log n) bits of redundancy which can be reconstructed from poly(log n) traces for a small constant deletion probability.This point of view naturally leads to the problem of coded trace reconstruction: The goal is to design high rate, efficiently encodable codes whose codewords can be efficiently reconstructed with high probability from very few traces with constant deletion probability. Here, "high rate" refers to a rate approaching 1 as the block length increases. We remark that in such a case, the number of traces must grow with the block length of the code. Coded trace reconstruction is also closely related to and motivated by the read process in portable DNA-based data storage systems, which we discuss below.Motivation A practical motivation for coded trace reconstruction comes from portable DNA-based data storage systems using DNA nanopores, first introduced in [13]. In DNA-based storage, a block of user-defined data is first encoded over the nucleotide alphabet {A, C, G, T }, and then transformed into moderately long strands of DNA through a DNA synthesis process. For ease of synthesis, the DNA strands are usually encoded to have balanced GC-content, so that the fraction of {A, T } and {G, C} bases is roughly the same. To recover the block of data, the associated strand of DNA is sequenced with nanopores, resulting in multiple corrupted reads of its encoding. Although the errors encountered during nanopore sequencing include both deletions/insertions as well as substitution errors, careful read preprocessing alignment [13] allows the processed reads to be viewed as traces of the data block's encoding. As a result, recovering the data block in question can be cast in the setting of trace reconstruction. Due to sequencing delay constraints 1 , it is of great ...

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“…Codes dealing with insertion/deletion errors were also studied in [11]. Codes that can correct a total of K substitution errors were studied in [12] using the sphere packing arguments, which is essentially the same as the error ball arguments.…”

Section: Introductionmentioning

confidence: 99%

Sequence-Subset Distance and Coding for Error Control for DNA-based Data Storage

Song

Cai

Immink³

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes for DNA storage channel, a new metric, termed the sequence-subset distance, is introduced, which generalizes the Hamming distance to a distance function defined between any two sets of unordered vectors and helps to establish a uniform framework to design error correcting codes for DNA storage channel. We further introduce a family of error correcting codes, referred to as sequencesubset codes, for DNA storage and show that the error-correcting ability of such codes is completely determined by their minimum distance. We derive some upper bounds on the size of the sequence-subset codes including a Singleton-like bound and a Plotkin-like bound. We also propose some constructions, which imply lower bounds on the size of such codes.

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On Coding Over Sliced Information

Cited by 21 publications

References 21 publications

Coding Over Sets for DNA Storage

Coding Over Sets for DNA Storage

Coded Trace Reconstruction

Sequence-Subset Distance and Coding for Error Control for DNA-based Data Storage

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