On Coding over Sliced Information

Sima, Jin; Raviv, Netanel; Bruck, Jehoshua

doi:10.48550/arxiv.1809.02716

Cited by 3 publications

(2 citation statements)

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“…Most related to our study is the work discussing channels with unordered input and output strands. Such channels have been discussed from a worst-case point of view in [11], [15], [16]. On the other hand, probabilistic channels have been discussed in [17], [18] for the case where there are no errors inside the strands [19] and for the case, where each strand is drawn exactly once [18].…”

Section: Introductionmentioning

confidence: 99%

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Lenz¹,

Welter²,

Puchinger³

2020

Preprint

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In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each strand is replicated many times. Third, the data is accessed in an uncontrollable manner, i.e., random strands are drawn from the medium and received, possibly with errors. As one of our results, we show that there is a significant gap between the channel capacity and the achievable rate of a standard concatenated code in which one strand corresponds to an inner block. This is in fact surprising as for other channels, such as q-ary symmetric channels, concatenated codes are known to achieve the capacity. We further propose a modified concatenated coding scheme by combining several strands into one inner block, which allows to narrow the gap and achieve rates that are close to the capacity.

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Section: Introductionmentioning

confidence: 99%

Achievable Rates of Concatenated Codes in DNA Storage under Substitution Errors

Lenz¹,

Welter²,

Puchinger³

2020

Preprint

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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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