On Levenshtein’s Channel and List Size in Information Retrieval

Junnila, Ville; Laihonen, Tero; Lehtilä, Tuomo

doi:10.1109/tit.2020.3016269

Cited by 13 publications

(33 citation statements)

References 20 publications

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“…Let C ⊆ Z n be a code with the minimum distance d k+,k− (C) = δ. Let N and τ be defined as in (10) and (11). Let Y = {y 1 , y 2 , .…”

Section: Algorithm 4 List Decoding Algorithmmentioning

confidence: 99%

“…In [10], the trade-off between the size of the minimum list and the number of different received noisy sequences has been analyzed for substitutions. Modifying the approach therein, we could give another list-decoding algorithm which reduces simultaneously the value of N and the size of L in Theorem 25, at the cost of the time complexity.…”

Section: Algorithm 4 List Decoding Algorithmmentioning

confidence: 99%

“…In the context of sequence reconstruction, a closely related problem is to construct a list from multiple received noisy sequences such that the transmitted sequence is included in the list. The trade-off between the size of the minimum list (the number of balls) and the number of different received noisy sequences (the maximum intersection / uncertainty) has been analyzed for substitutions [10] and for tandem-duplications [30].…”

Section: Introductionmentioning

confidence: 99%

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Sequence Reconstruction for Limited-Magnitude Errors

Wei¹,

Schwartz²

2021

Preprint

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Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in relation to the code's minimum distance. We also devise efficient reconstruction algorithms for various limitedmagnitude error parameter ranges. We then extend these algorithms to the list-reconstruction scheme, and show the trade-off between the asymptotic list size and the number of required channel outputs. These results apply to all codes, without any assumptions on the code structure. Finally, we also study linear reconstruction codes with small intersection, as well as show a connection to list-reconstruction codes for the tandem-duplication channel.

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“…Let C ⊆ Z n be a code with the minimum distance d k+,k− (C) = δ. Let N and τ be defined as in (10) and (11). Let Y = {y 1 , y 2 , .…”

Section: Algorithm 4 List Decoding Algorithmmentioning

confidence: 99%

Section: Algorithm 4 List Decoding Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sequence Reconstruction for Limited-Magnitude Errors

Wei¹,

Schwartz²

2021

Preprint

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“…Recently, the authors of [18] investigated the case where errors are combinations of single substitution and single insertion. Furthermore, they also Another recent variant of the Levenshtein sequence reconstruction problem was studied by the authors in [19]. Similar to our model, the authors consider the scenario where the number of reads is not sufficient to reconstruct a unique codeword.…”

Section: A Related Workmentioning

confidence: 99%

Coding for Sequence Reconstruction for Single Edits

Kiah

Nguyen

Yaakobi

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common setup assumes the codebook to be the entire space and the problem is to determine the minimum number of distinct reads that is required to reconstruct the transmitted codeword.Motivated by modern storage devices, we study a variant of the problem where the number of noisy reads N is fixed. Specifically, we design reconstruction codes that reconstruct a codeword from N distinct noisy reads. We focus on channels that introduce single edit error (i.e. a single substitution, insertion, or deletion) and their variants, and design reconstruction codes for all values of N . In particular, for the case of a single edit, we show that as the number of noisy reads increases, the number of redundant bits required can be gracefully reduced from log n + O(1) to log log n + O(1), and then to O(1), where n denotes the length of a codeword. We also show that the redundancy of certain reconstruction codes is within one bit of optimality.

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“…People are used to combining two or more language words in oral or written texts, which leads to more information data being colloquial and re ned, which brings great di culty to the rapid retrieval of network portal information [1]. At the same time, because the network portal information is also a ected by the noise channel, the retrieval data is more complex, easy to reduce the retrieval e ciency, and cannot meet user needs [2]. erefore, the rapid retrieval method of network portal information has become a hot issue in the eld of computer data processing and has received wide attention.…”

Section: Introductionmentioning

confidence: 99%

Fast Retrieval Method of Portal Information Based on a Chaotic Genetic Algorithm

Zhao

Tai

2022

Mathematical Problems in Engineering

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The traditional retrieval method cannot respond to the influence of the change in the portal website’s information characteristics, resulting in low efficiency. In this regard, a fast information retrieval method based on a chaotic genetic algorithm is proposed. According to the relevant theory of association rules, the correlation between information data of dynamic portal websites is calculated; different portal website information is retrieved based on the Markov model output; a chaotic genetic algorithm is used to fuse different portal website information. The information data constructs a decision tree for rapid retrieval of portal information, uses the vector form to express the characteristics of portal information, and finally realizes the rapid retrieval of portal information. The experimental results show that the designed method takes up to 15 ms when the sample complexity is high, which shows that the designed method has high efficiency and is of great significance in practical applications.

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On Levenshtein’s Channel and List Size in Information Retrieval

Cited by 13 publications

References 20 publications

Sequence Reconstruction for Limited-Magnitude Errors

Sequence Reconstruction for Limited-Magnitude Errors

Coding for Sequence Reconstruction for Single Edits

Fast Retrieval Method of Portal Information Based on a Chaotic Genetic Algorithm

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