Syndrome Compression for Optimal Redundancy Codes

Sima, Jin; Gabrys, Ryan; Bruck, Jehoshua

doi:10.1109/isit44484.2020.9174009

Cited by 17 publications

(8 citation statements)

References 16 publications

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“…In order to construct error-correcting codes by applying the syndrome compression technique [35], we first introduce some auxiliary definitions and a theorem.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…As stated in Section III, our code for correcting duplications and substitutions is a subset of irreducible strings of a given length. In this section, we construct this subset by applying the syndrome compression technique [35], where we will make use of the size of the irreducible-confusable set B ≤p Irr (x) derived in Section III. In this section, unless otherwise stated, we assume that both q ≥ 4 and p are constant.…”

Section: Low-redundancy Error-correcting Codesmentioning

confidence: 99%

“…Then using syndrome compression, we compute and append to x a "parity" sequence r to help correct errors that occur in x. Syndrome compression has recently been used to provide explicit constructions for correcting a wide variety of errors with redundancy as low as roughly twice the Gilbert-Varshamov bound [35]- [38]. Another challenge arises from the interaction between the errors.…”

Section: Introductionmentioning

confidence: 99%

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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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“…In order to construct error-correcting codes by applying the syndrome compression technique [35], we first introduce some auxiliary definitions and a theorem.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Section: Low-redundancy Error-correcting Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Tang¹,

Wang²,

Liang³

et al. 2022

Preprint

Self Cite

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show abstract

“…In [11], Lenz and Polyanskii presented codes that correct consecutive bursts of deletions of length at most t that required only log n + O(log log n) bits of redundancy. The best-known systematic codes can be found in [12]. A summary of these results is included in Table I.…”

Section: Introductionmentioning

confidence: 99%

“…Since our approach uses a different technique than the one from [13], it may be of independent interest. ≤ 2 log n + 1 [10] = t log n + O(log log n) [10] ≤ t (t − 1) log n + O(log log n) [11] ≤ t log n + O(log log n) [12] ≤ t 4 log n + o(log n) The remainder of this article is outlined as follows. Section II presents the notations and two well-known deletion correcting codes used throughout this paper as well as some preliminary results.…”

Section: Introductionmentioning

confidence: 99%

Non-binary Codes for Correcting a Burst of at Most 2 Deletions

Wang

Sima

Farnoud

2021

2021 IEEE International Symposium on Information Theory (ISIT)

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The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most t deletions in non-binary sequences. We first propose a non-binary code correcting a burst of at most 2 deletions for q-ary alphabets. Afterwards, we extend this result to the case where the length of the burst can be at most t where t is a constant. Finally, we consider the setup where the sequences that are transmitted are permutations. The proposed codes are the largest known for their respective parameter regimes.

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