5 Search Results for "Gabrys, Ryan"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.30
New Bounds for Circular Trace Reconstruction

Authors: Arnav Burudgunte, Paul Valiant, and Hongao Wang

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
The "trace reconstruction" problem asks, given an unknown binary string x and a channel that repeatedly returns "traces" of x with each bit randomly deleted with some probability p, how many traces are needed to recover x? There is an exponential gap between the best known upper and lower bounds for this problem. Many variants of the model have been introduced in hopes of motivating or revealing new approaches to narrow this gap. We study the variant of circular trace reconstruction introduced by Narayanan and Ren (ITCS 2021), in which traces undergo a random cyclic shift in addition to random deletions. We show an improved lower bound of Ω̃(n⁵) for circular trace reconstruction. This contrasts with the (previously) best known lower bounds of Ω̃(n³) in the circular case and Ω̃(n^{3/2}) in the linear case. Our bound shows the indistinguishability of traces from two sparse strings x,y that each have a constant number of nonzeros. Can this technique be extended significantly? How hard is it to reconstruct a sparse string x under a cyclic deletion channel? We resolve these questions by showing, using Fourier techniques, that Õ(n⁶) traces suffice for reconstructing any constant-sparse string in a circular deletion channel, in contrast to the best known upper bound of exp(Õ(n^{1/3})) for general strings in the circular deletion channel. This shows that new algorithms or new lower bounds must focus on non-constant-sparse strings.
Cite as

Arnav Burudgunte, Paul Valiant, and Hongao Wang. New Bounds for Circular Trace Reconstruction. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{burudgunte_et_al:LIPIcs.ITCS.2026.30,
  author =	{Burudgunte, Arnav and Valiant, Paul and Wang, Hongao},
  title =	{{New Bounds for Circular Trace Reconstruction}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{30:1--30:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.30},
  URN =		{urn:nbn:de:0030-drops-253176},
  doi =		{10.4230/LIPIcs.ITCS.2026.30},
  annote =	{Keywords: Trace reconstruction, algorithmic statistics, Fourier analysis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.3
Near-Optimal Trace Reconstruction for Mildly Separated Strings

Authors: Anders Aamand, Allen Liu, and Shyam Narayanan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In the trace reconstruction problem our goal is to learn an unknown string x ∈ {0,1}ⁿ given independent traces of x. A trace is obtained by independently deleting each bit of x with some probability δ and concatenating the remaining bits. It is a major open question whether the trace reconstruction problem can be solved with a polynomial number of traces when the deletion probability δ is constant. The best known upper bound and lower bounds are respectively exp(Õ(n^{1/5})) [Zachary Chase, 2021a] and ̃ Ω(n^{3/2}) [Zachary Chase, 2021b]. Our main result is that if the string x is mildly separated, meaning that the number of zeros between any two ones in x is at least polylog n, and if δ is a sufficiently small constant, then the trace reconstruction problem can be solved with O(n log n) traces and in polynomial time.
Cite as

Anders Aamand, Allen Liu, and Shyam Narayanan. Near-Optimal Trace Reconstruction for Mildly Separated Strings. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aamand_et_al:LIPIcs.ICALP.2025.3,
  author =	{Aamand, Anders and Liu, Allen and Narayanan, Shyam},
  title =	{{Near-Optimal Trace Reconstruction for Mildly Separated Strings}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.3},
  URN =		{urn:nbn:de:0030-drops-233801},
  doi =		{10.4230/LIPIcs.ICALP.2025.3},
  annote =	{Keywords: Trace Reconstruction, deletion channel, sample complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.60
Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets

Authors: Roni Con, Zeyu Guo, Ray Li, and Zihan Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that, for any ε > 0 and positive integers n and k, with high probability, random Reed-Solomon codes of length n and dimension k can correct (1-ε)n-2k+1 adversarial insdel errors over alphabets of size n+2^{poly(1/ε)}k. This significantly improves upon the alphabet size demonstrated in the work of Con, Shpilka, and Tamo (IEEE TIT, 2023), who showed the existence of Reed-Solomon codes with exponential alphabet size Õ(binom(n,2k-1)²) precisely achieving the half-Singleton bound. Our methods are inspired by recent works on list-decoding Reed-Solomon codes. Brakensiek-Gopi-Makam (STOC 2023) showed that random Reed-Solomon codes are list-decodable up to capacity with exponential-sized alphabets, and Guo-Zhang (FOCS 2023) and Alrabiah-Guruswami-Li (STOC 2024) improved the alphabet-size to linear. We achieve a similar alphabet-size reduction by similarly establishing strong bounds on the probability that certain random rectangular matrices are full rank. To accomplish this in our insdel context, our proof combines the random matrix techniques from list-decoding with structural properties of Longest Common Subsequences.
Cite as

Roni Con, Zeyu Guo, Ray Li, and Zihan Zhang. Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 60:1-60:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{con_et_al:LIPIcs.ICALP.2025.60,
  author =	{Con, Roni and Guo, Zeyu and Li, Ray and Zhang, Zihan},
  title =	{{Random Reed-Solomon Codes Achieve the Half-Singleton Bound for Insertions and Deletions over Linear-Sized Alphabets}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{60:1--60:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.60},
  URN =		{urn:nbn:de:0030-drops-234372},
  doi =		{10.4230/LIPIcs.ICALP.2025.60},
  annote =	{Keywords: coding theory, error-correcting codes, Reed-Solomon codes, insdel, insertion-deletion errors, half-Singleton bound}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.8
Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

Authors: Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage. One of the most basic versions of this problem was settled more than 50 years ago by Levenshtein, who proved that binary Varshamov-Tenengolts codes correct one arbitrary edit error, i.e., one deletion or one substitution, with nearly optimal redundancy. However, this approach fails to extend to many simple and natural variations of the binary single-edit error setting. In this work, we make progress on the code design problem above in three such variations: - We construct linear-time encodable and decodable length-n non-binary codes correcting a single edit error with nearly optimal redundancy log n+O(log log n), providing an alternative simpler proof of a result by Cai, Chee, Gabrys, Kiah, and Nguyen (IEEE Trans. Inf. Theory 2021). This is achieved by employing what we call weighted VT sketches, a new notion that may be of independent interest. - We show the existence of a binary code correcting one deletion or one adjacent transposition with nearly optimal redundancy log n+O(log log n). - We construct linear-time encodable and list-decodable binary codes with list-size 2 for one deletion and one substitution with redundancy 4log n+O(log log n). This matches the existential bound up to an O(log log n) additive term.
Cite as

Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu. Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gabrys_et_al:LIPIcs.APPROX/RANDOM.2022.8,
  author =	{Gabrys, Ryan and Guruswami, Venkatesan and Ribeiro, Jo\~{a}o and Wu, Ke},
  title =	{{Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  URN =		{urn:nbn:de:0030-drops-171302},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  annote =	{Keywords: Synchronization errors, Optimal redundancy, Explicit codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.17
Accelerating Polarization via Alphabet Extension

Authors: Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
Polarization is an unprecedented coding technique in that it not only achieves channel capacity, but also does so at a faster speed of convergence than any other technique. This speed is measured by the "scaling exponent" and its importance is three-fold. Firstly, estimating the scaling exponent is challenging and demands a deeper understanding of the dynamics of communication channels. Secondly, scaling exponents serve as a benchmark for different variants of polar codes that helps us select the proper variant for real-life applications. Thirdly, the need to optimize for the scaling exponent sheds light on how to reinforce the design of polar code. In this paper, we generalize the binary erasure channel (BEC), the simplest communication channel and the protagonist of many polar code studies, to the "tetrahedral erasure channel" (TEC). We then invoke Mori-Tanaka’s 2 × 2 matrix over 𝔽_4 to construct polar codes over TEC. Our main contribution is showing that the dynamic of TECs converges to an almost-one-parameter family of channels, which then leads to an upper bound of 3.328 on the scaling exponent. This is the first non-binary matrix whose scaling exponent is upper-bounded. It also polarizes BEC faster than all known binary matrices up to 23 × 23 in size. Our result indicates that expanding the alphabet is a more effective and practical alternative to enlarging the matrix in order to achieve faster polarization.
Cite as

Iwan Duursma, Ryan Gabrys, Venkatesan Guruswami, Ting-Chun Lin, and Hsin-Po Wang. Accelerating Polarization via Alphabet Extension. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{duursma_et_al:LIPIcs.APPROX/RANDOM.2022.17,
  author =	{Duursma, Iwan and Gabrys, Ryan and Guruswami, Venkatesan and Lin, Ting-Chun and Wang, Hsin-Po},
  title =	{{Accelerating Polarization via Alphabet Extension}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.17},
  URN =		{urn:nbn:de:0030-drops-171393},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.17},
  annote =	{Keywords: polar code, scaling exponent}
}
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