Torn-Paper Coding

Shomorony, Ilan; Vahid, Alireza

doi:10.1109/tit.2021.3120920

Cited by 13 publications

(6 citation statements)

References 37 publications

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“…We can then optimize over integer values of m to obtain the required achievable rates. See [21] for more details. This rate is compared to C TPC in Figure 8.…”

Section: Index-based Coding Via Interleaving For the Torn-paper Channelmentioning

confidence: 99%

“…Here, the zero-error capacity is essentially the capacity under the worstcase error of this genie channel. For probabilistic channels like the standard TPC [21], there is a non-zero probability of breaking a codeword into pieces of size 1. This implies that the zero-error capacity is zero (since breaking a codeword into pieces of size 1 converts the channel into the permutation channel [16], for which the capacity with standard normalization is zero).…”

Section: Index-based Coding Via Unique Headers For the Torn-paper Cha...mentioning

confidence: 99%

“…The two channel models we will consider are inspired by the aforementioned practical considerations (1) and ( 2) and are illustrated in Figure 2. We refer to these two channels as the Torn-Paper Channel (TPC) [20][21][22], shown in Figure 2(a), and the Shotgun Sequencing Channel (SSC) [23,24], shown in Figure 2(b). The TPC breaks the input sequence x n into pieces of random sizes, and a subset of these pieces is observed at the output.…”

Section: Introductionmentioning

confidence: 99%

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An Information Theory for Out-of-Order Media With Applications in DNA Data Storage

Ravi,

Vahid,

Shomorony

2024

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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Recent advancements in DNA-based storage prototypes focus on encoding information across multiple DNA molecules. This approach utilizes high-throughput sequencing technologies, leading to outputs that are out-of-order. We study the shuffling channel, where input codewords are split into fixed-size fragments. We show that achieving channel capacity uses index-based coding, which assigns unique indices to each fragment. We also introduce two more complex channels, which aim to model popular sequencing strategies in DNA sequencing. In the torn-paper channel, the input codeword is torn up into fragments of random sizes, while in the shotgun sequencing channel, fixed-length random substrings of the input codeword are observed at the output. In both of these channels, the lack of ordering cannot be circumvented by simply adding unique indices to the fragments. We show how the capacity of both of these channels can be achieved using random codes. We introduce and analyze code constructions based on index sequences. While these codes are computationally efficient, they are not capacityachieving, and we leave the questions of finding efficient capacityachieving codes for these settings as open problems.

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“…We can then optimize over integer values of m to obtain the required achievable rates. See [21] for more details. This rate is compared to C TPC in Figure 8.…”

Section: Index-based Coding Via Interleaving For the Torn-paper Channelmentioning

confidence: 99%

Section: Index-based Coding Via Unique Headers For the Torn-paper Cha...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Information Theory for Out-of-Order Media With Applications in DNA Data Storage

Ravi,

Vahid,

Shomorony

2024

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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“…Notably, when observations are comprised of unordered consecutive substrings, two distinct models have received significant interest in the past decade due to applications in DNA-or polymer-based storage systems, resulting from contemporary sequencing technologies [4], [12], [26]. The first is the reconstruction from substring-compositions problem [1], [4], [10], [14], [17], [23], [25], [26], [32], [34], [38], [39] (including extensions for erroneous observations [5], [12], [23], [39]), which arises from an idealized assumption of full overlap (and uniform coverage) in read substrings; the second is the torn-paper problem [2], [27], [28], [35] (a problem closely related to the shuffling channel [15], [18], [33], [37]), which results from an assumption of no overlap. In applications, the distinction models the question of whether the complete information string may be replicated and uniformly segmented for sequencing, or if segmentation occurs adversarially in the medium prior to sequencing.…”

Section: Introductionmentioning

confidence: 99%

Multi-strand Reconstruction from Substrings

Yehezkeally

Marcovich

Yaakobi

2021

2021 IEEE Information Theory Workshop (ITW)

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This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which all substrings of predefined lengths are read or substrings are read with no overlap for the single string case, this work studies two extensions of this paradigm. The first extension considers the setup in which consecutive substrings are read with some given minimum overlap. First, an upper bound is provided on the attainable rates of codes that guarantee unique reconstruction. Then, efficient constructions of codes that asymptotically meet that upper bound are presented. In the second extension, we study the setup where multiple strings are reconstructed together. Given the number of strings and their length, we first derive a lower bound on the read substrings' length ℓ that is necessary for the existence of multi-strand reconstruction codes with non-vanishing rates. We then present two constructions of such codes and show that their rates approach 1 for values of ℓ that asymptotically behave like the lower bound.

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“…Other related problem settings include: permutation channels [15], [16], [21], [28], [33], which consider string errors only, and torn paper coding [3], [25]. See [24] for a broader survey of the related problems.…”

Section: Introductionmentioning

confidence: 99%

Robust Indexing - Optimal Codes for DNA Storage

Sima

Raviv

Bruck

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In this paper, we address this problem and present an order-wise optimal construction of codes that are capable of correcting multiple substitution, deletion, and insertion errors for this channel model. The key ingredient in the code construction is a technique we call robust indexing: simultaneously assigning indices to unordered strings (hence, creating order) and also embedding information in these indices. The encoded indices are resilient to substitution, deletion, and insertion errors, and therefore, so is the entire code.

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Torn-Paper Coding

Cited by 13 publications

References 37 publications

An Information Theory for Out-of-Order Media With Applications in DNA Data Storage

An Information Theory for Out-of-Order Media With Applications in DNA Data Storage

Multi-strand Reconstruction from Substrings

Robust Indexing - Optimal Codes for DNA Storage

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