Single-Error Detection and Correction for Duplication and Substitution Channels

Tang, Yuanyuan; Yehezkeally, Yonatan; Schwartz, Moshe; Farnoud, Farzad

doi:10.1109/tit.2020.3006228

Cited by 21 publications

(15 citation statements)

References 12 publications

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“…Finally, if the total number of duplications is limited, restricting codewords to irreducible sequences will be inefficient, although a combination of irreducible sequences and codes in the 1 -metric have been found to be of use in the related problem of correcting only exact duplications [7]. Another possible direction is the use of constrained codes, similar to [16], to decrease the variety of the error types that may be encountered, thereby simplifying code construction. We note however that such an approach will likely incur a rate penalty.…”

Section: Discussionmentioning

confidence: 99%

“…Additionally both codes have the same asymptotic rate (given in (1) for large k), and in this sense the code proposed here is asymptotically optimal, although it is not clear whether (2k + 4) log q n is the best possible redundancy. For the alphabet size q ∈ {3, 4, 5} and the duplication length k = 3, Figure 2 shows the lower bound of the code rate as the length n of codewords ranges from 100 to 400, based on (34), (16) and [5].…”

Section: Error-correcting Codes For Noisy Duplication Channelsmentioning

confidence: 99%

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Error-correcting Codes for Noisy Duplication Channels

Tang

Farnoud

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing data storage needs. Compared to conventional storage media, however, data stored in DNA is subject to a wider range of errors resulting from various processes involved in the data storage pipeline. In this paper, we consider correcting duplication errors for both exact and noisy tandem duplications of a given length k. An exact duplication inserts a copy of a substring of length k of the sequence immediately after that substring, e.g., ACGT → ACGACGT, where k = 3, while a noisy duplication inserts a copy suffering from substitution noise, e.g., ACGT → ACGATGT. Specifically, we design codes that can correct any number of exact duplication and one noisy duplication errors, where in the noisy duplication case the copy is at Hamming distance 1 from the original. Our constructions rely upon recovering the duplication root of the stored codeword. We characterize the ways in which duplication errors manifest in the root of affected sequences and design efficient codes for correcting these error patterns. We show that the proposed construction is asymptotically optimal, in the sense that it has the same asymptotic rate as optimal codes correcting exact duplications only.

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Section: Discussionmentioning

confidence: 99%

Section: Error-correcting Codes For Noisy Duplication Channelsmentioning

confidence: 99%

Error-correcting Codes for Noisy Duplication Channels

Tang

Farnoud

2019

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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“…Fix some string-duplication system S = S(Σ, s, T ). Depending on the application, one can view S in two ways: either as a generative model which describes what possible strings may be derived from s (e.g., see [2], [6], [9], [12], [15], [25]), or as a channel which describes what corrupted versions of the transmitted s may be received (e.g., see [16]- [18], [20], [32], [34], [38]- [40]). While the latter view calls for the construction of suitably tailored error-correcting codes, the former inspires the following properties of S to be studied.…”

Section: Preliminariesmentioning

confidence: 99%

“…Other codes that correct a prescribed number of duplications were constructed in [17], [18], [20], [40], addressing several duplication types. Additional codes that are capable of correcting a mixture of tandem duplications and substitutions or edits were described in [32]- [34]. Finally, some Levenshtein-reconstruction problems for duplications were studied in [38], [39].…”

Section: Introductionmentioning

confidence: 99%

On the Reverse-Complement String-Duplication System

Ben-Tolila¹,

Schwartz²

2021

Preprint

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Motivated by DNA storage in living organisms, and by known biological mutation processes, we study the reverse-complement string-duplication system. We fully classify the conditions under which the system has full expressiveness, for all alphabets and all fixed duplication lengths. We then focus on binary systems with duplication length 2 and prove that they have full capacity, yet surprisingly, have zero entropy-rate. Finally, by using binary single burst-insertion correcting codes, we construct codes that correct a single reverse-complement duplication of odd length, over any alphabet. The redundancy (in bits) of the constructed code does not depend on the alphabet size.

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“…Lenz et al [30] provided a construction for codes that can correct one PD error. In [31], codes were given which can correct a combination of TD errors of fixed length k and at most one substitution error. Constructing codes which can correct multiple PD errors or a combination of TD and PD errors remains an open problem.…”

Section: Introductionmentioning

confidence: 99%

Construction of Duplication Correcting Codes

2020

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Palindromic duplication (PD) and tandem duplication (TD) errors can occur when the DNA of a living organism is used to store data. In this work, we construct codes which can correct any number of PD errors of fixed length k where k = 2, 3. Codes are also constructed to correct a combination of TD errors of fixed length k and PD errors of fixed length k where k = 2, 3. We introduce k-clamp free irreducible words and use them to construct codes which can correct any combination of k-TD and k-PD errors where k = 2, 3. The extension of these constructions to k > 3 is conjectured. INDEX TERMSError correction codes, DNA computing, data storage systems, error analysis, duplication error. MORTEZA ESMAEILI received the M.S. degree in mathematics from the Teacher Training University of Tehran, Iran, in 1988, and the Ph.D. degree in mathematics (coding theory) from Car-

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Single-Error Detection and Correction for Duplication and Substitution Channels

Cited by 21 publications

References 12 publications

Error-correcting Codes for Noisy Duplication Channels

Error-correcting Codes for Noisy Duplication Channels

On the Reverse-Complement String-Duplication System

Construction of Duplication Correcting Codes

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