Optimal Codes for the q-ary Deletion Channel

Sima, Jin; Gabrys, Ryan; Bruck, Jehoshua

doi:10.1109/isit44484.2020.9174241

Cited by 23 publications

(4 citation statements)

References 16 publications

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“…In each step of the construction, we carefully ensured that the resulting sequence is still irreducible. The additional redundancy compared to the codes correcting duplications only [10] is 8p(log q n)(1 + o(1)), with the number of edits p and the alphabet size q being constants, which is at most a factor of 2 away from the lowestredundancy codes for correcting p edits only [37] and a factor of 4 away from the GV bound given in Theorem 14. The encoding and decoding processes have polynomial time complexities.…”

Section: Discussionmentioning

confidence: 96%

“…Compared to the explicit code for short duplications only [10], the proposed code corrects ≤ p edits in addition to the duplications at the extra cost of roughly 8p(log q n)(1 + o(1)) symbols of redundancy for q ≥ 4, and achieves the same asymptotic code rate. We note that the state-of-the-art redundancy for correcting p edits is no less than 4p log q n(1 + o(1)) [37]. Time complexities of both the encoding and decoding processes are polynomial when p is a constant.…”

Section: Introductionmentioning

confidence: 95%

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Low-redundancy codes for correcting multiple short-duplication and edit errors

Tang¹,

Wang²,

Liang³

et al. 2022

Preprint

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Due to its higher data density, longevity, energy efficiency, and ease of generating copies, DNA is considered a promising storage technology for satisfying future needs. However, a diverse set of errors including deletions, insertions, duplications, and substitutions may arise in DNA at different stages of data storage and retrieval. The current paper constructs error-correcting codes for simultaneously correcting short (tandem) duplications and at most p edits, where a short duplication generates a copy of a substring with length ≤ 3 and inserts the copy following the original substring, and an edit is a substitution, deletion, or insertion. Compared to the state-of-the-art codes for duplications only, the proposed codes correct up to p edits (in addition to duplications) at the additional cost of roughly 8p(log q n)(1 + o(1)) symbols of redundancy, thus achieving the same asymptotic rate, where q ≥ 4 is the alphabet size and p is a constant. Furthermore, the time complexities of both the encoding and decoding processes are polynomial when p is a constant with respect to the code length.

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Section: Discussionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 95%

Low-redundancy codes for correcting multiple short-duplication and edit errors

Tang¹,

Wang²,

Liang³

et al. 2022

Preprint

Self Cite

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“…If D t (c) ∩ D t (c ) = ∅ for any two distinct sequences c, c ∈ C, we say C is a q-ary t-deletion correcting code. There are some known results on nonbinary t-deletion correcting codes with low redundancy [20], [40].…”

Section: A Variant Of the Absorption Channel And Its Connection With ...mentioning

confidence: 99%

Codes Over Absorption Channels

Zuo¹,

Elishco²

2023

Preprint

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In this paper, we present a novel communication channel, called the absorption channel, inspired by information transmission in neurons. Our motivation comes from in-vivo nano-machines, emerging medical applications, and brain-machine interfaces that communicate over the nervous system. Another motivation comes from viewing our model as a specific deletion channel, which may provide a new perspective and ideas to study the general deletion channel.For any given finite alphabet, we give codes that can correct absorption errors. For the binary alphabet, the problem is relatively trivial and we can apply binary (multiple-) deletion correcting codes. For single-absorption error, we prove that the Varshamov-Tenengolts codes can provide a near-optimal code in our setting. When the alphabet size q is at least 3, we first construct a single-absorption correcting code whose redundancy is at most 3 log q (n) + O(1). Then, based on this code and ideas introduced in [1], we give a second construction of single-absorption correcting codes with redundancy log q (n) + 12 log q log q (n) + O(1), which is optimal up to an O log q log q (n) .Finally, we apply the syndrome compression technique with pre-coding to obtain a subcode of the single-absorption correcting code. This subcode can combat multiple-absorption errors and has low redundancy. For each setup, efficient encoders and decoders are provided.

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“…However, designing q -ary VT codes that can correct multiple deletion or insertion errors has been an interesting problem [ 17 ]. Recently, there were some works [ 18 , 19 , 20 , 21 ] focused on code design to correct exact multiple errors but the efficient design for q -ary codes (or even quaternary codes) that can correct a burst of at most b deletion or insertion errors is still an open problem. The authors of [ 22 ] proposed a non-binary code correcting at most two consecutive deletions with redundancy

.…”

Section: Introductionmentioning

confidence: 99%

A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

Khuat

Kim

2021

Entropy

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Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.

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Optimal Codes for the q-ary Deletion Channel

Cited by 23 publications

References 16 publications

Low-redundancy codes for correcting multiple short-duplication and edit errors

Low-redundancy codes for correcting multiple short-duplication and edit errors

Codes Over Absorption Channels

A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage

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