Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

Cheng, Kuan; Jin, Zhengzhong; Li, Xin; Ke, Wu

doi:10.1109/focs.2018.00028

Cited by 64 publications

(61 citation statements)

References 23 publications

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“…Our efficient randomized hashing scheme takes any n-bit file F and for any k computes an optimal sized O(k log n k )-bit summary from which one can reconstruct F given a related Supported in part by NSF grants CCF-1618280, CCF-1814603, CCF-1527110, NSF CAREER award CCF-1750808, and a Sloan Research Fellowship. 1 The same derandomization result was simultaneously and independently discovered by [3,Cheng, Jin, Li and Wu; FOCS '18]. Both works were put on arxiv days apart [4], [5].…”

Section: Introductionmentioning

confidence: 62%

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Optimal Document Exchange and New Codes for Insertions and Deletions

Haeupler

2019

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)

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Section: Introductionmentioning

confidence: 62%

“…This paper solely focuses on such single-round document exchange schemes. For simplicity, like all other prior works, we assume that a good upper bound k on the edit distance ED(F, F ′ ) is known 3 .…”

Section: Introductionmentioning

confidence: 99%

Optimal Document Exchange and New Codes for Insertions and Deletions

Haeupler

2019

2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)

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“…It is easy to show that there exist families of codes which correct an fraction of deletions and insertions with rate approaching 1 as → 0. In fact, almost optimal explicit constructions of efficiently decodable codes of this type are known [26,27].…”

Section: Discussionmentioning

confidence: 99%

Sharp Analytical Capacity Upper Bounds for Sticky and Related Channels

Cheraghchi

Ribeiro

2019

IEEE Trans. Inform. Theory

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We study natural examples of binary channels with synchronization errors. These include the duplication channel, which independently outputs a given bit once or twice, and geometric channels that repeat a given bit according to a geometric rule, with or without the possibility of bit deletion. We apply the general framework of Cheraghchi (STOC 2018) to obtain sharp analytical upper bounds on the capacity of these channels. Previously, upper bounds were known via numerical computations involving the computation of finite approximations of the channels by a computer and then using the obtained numerical results to upper bound the actual capacity. While leading to sharp numerical results, further progress on the full understanding of the channel capacity inherently remains elusive using such methods. Our results can be regarded as a major step towards a complete understanding of the capacity curves. Quantitatively, our upper bounds sharply approach, and in some cases surpass, the bounds that were previously only known by purely numerical methods. Among our results, we notably give a completely analytical proof that, when the number of repetitions per bit is geometric (supported on {0, 1, 2, . . . }) with mean growing to infinity, the channel capacity remains substantially bounded away from 1.

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“…The following result is relevant to our analysis. Lemma 9 ([41,42]). For every m and t < m there exists an efficiently encodable and decodable systematic code C edit ⊆ {0, 1} m+r with encoder Enc edit : {0, 1} m → {0, 1} m+r and redundancy r = O t log 2 m t + t that can efficiently correct up to t edit errors.…”

Section: Nearly-optimal Systematic Codes For Edit Errorsmentioning

confidence: 99%

“…We make this statement rigorous in the following lemma. We note that the technique in the lemma below has already been used in [42] to obtain strings satisfying related properties, such as substring-uniqueness, with high probability.…”

Section: Low Redundancy Codes Reconstructable From Polynomially Many mentioning

confidence: 99%

Coded Trace Reconstruction

Cheraghchi

Ribeiro

Gabrys

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of coded trace reconstruction, the design and analysis of high-rate efficiently encodable codes that can be efficiently decoded with high probability from few reads (also called traces) corrupted by edit errors. Codes used in current portable DNA-based storage systems with nanopore sequencers are largely based on heuristics, and have no provable robustness or performance guarantees even for an error model with i.i.d. deletions and constant deletion probability. Our work is a first step towards the design of efficient codes with provable guarantees for such systems. We consider a constant rate of i.i.d. deletions, and perform an analysis of marker-based code-constructions. This gives rise to codes with redundancy O(n/ log n) (resp. O(n/ log log n)) that can be efficiently reconstructed from exp(O(log 2/3 n)) (resp. exp(O(log log n) 2/3 )) traces, where n is the message length. Then, we give a construction of a code with O(log n) bits of redundancy that can be efficiently reconstructed from poly(n) traces if the deletion probability is small enough. Finally, we show how to combine both approaches, giving rise to an efficient code with O(n/ log n) bits of redundancy which can be reconstructed from poly(log n) traces for a small constant deletion probability.This point of view naturally leads to the problem of coded trace reconstruction: The goal is to design high rate, efficiently encodable codes whose codewords can be efficiently reconstructed with high probability from very few traces with constant deletion probability. Here, "high rate" refers to a rate approaching 1 as the block length increases. We remark that in such a case, the number of traces must grow with the block length of the code. Coded trace reconstruction is also closely related to and motivated by the read process in portable DNA-based data storage systems, which we discuss below.Motivation A practical motivation for coded trace reconstruction comes from portable DNA-based data storage systems using DNA nanopores, first introduced in [13]. In DNA-based storage, a block of user-defined data is first encoded over the nucleotide alphabet {A, C, G, T }, and then transformed into moderately long strands of DNA through a DNA synthesis process. For ease of synthesis, the DNA strands are usually encoded to have balanced GC-content, so that the fraction of {A, T } and {G, C} bases is roughly the same. To recover the block of data, the associated strand of DNA is sequenced with nanopores, resulting in multiple corrupted reads of its encoding. Although the errors encountered during nanopore sequencing include both deletions/insertions as well as substitution errors, careful read preprocessing alignment [13] allows the processed reads to be viewed as traces of the data block's encoding. As a result, recovering the data block in question can be cast in the setting of trace reconstruction. Due to sequencing delay constraints 1 , it is of great ...

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Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

Cited by 64 publications

References 23 publications

Optimal Document Exchange and New Codes for Insertions and Deletions

Optimal Document Exchange and New Codes for Insertions and Deletions

Sharp Analytical Capacity Upper Bounds for Sticky and Related Channels

Coded Trace Reconstruction

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