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Documents authored by Zhang, Zihan

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.43
Unique Decoding of Reed–Solomon and Related Codes for Semi-Adversarial Errors

Authors: Joshua Brakensiek, Yeyuan Chen, Manik Dhar, and Zihan Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Motivated by recent developments in coding theory, particular in list-decoding, we introduce a new error model which we call semi-adversarial errors. This error model bridges between fully random errors and fully adversarial errors by allowing some symbols of a message to be corrupted by an adversary while others are replaced with uniformly random symbols. As our main quest, we seek to understand optimal efficient unique decoding algorithms in the semi-adversarial model. For interleaved Reed-Solomon (IRS), folded Reed-Solomon (FRS) and univariate multiplicity codes, we design decoding algorithms running in near-linear time for most mixtures of random and adversarial errors. Our analysis matches the information-theoretic optimum for semi-adversarial errors. Our algorithm for interleaved Reed-Solomon codes is an improved implementation of the decoding algorithm by Bleichenbacher-Kiayias-Yung (BKY) for fully random errors. We use a novel monomial-tracking technique to analyze its performance in this new semi-adversarial errors. Inspired by the BKY algorithm, we use novel interpolations to extend our approach to the settings of folded Reed-Solomon and multiplicity codes, resulting in fast algorithms for unique decoding against semi-adversarial errors. Our new decoders for FRS and multiplicity codes replace the sophisticated root-finding step in traditional algorithms, such as the Guruswami-Wang algorithm, with a straightforward polynomial long division. Analysis of these algorithms requires more robust monomial-tracking arguments than IRS codes.
Cite as

Joshua Brakensiek, Yeyuan Chen, Manik Dhar, and Zihan Zhang. Unique Decoding of Reed–Solomon and Related Codes for Semi-Adversarial Errors. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brakensiek_et_al:LIPIcs.ICALP.2026.43,
  author =	{Brakensiek, Joshua and Chen, Yeyuan and Dhar, Manik and Zhang, Zihan},
  title =	{{Unique Decoding of Reed–Solomon and Related Codes for Semi-Adversarial Errors}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{43:1--43:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.43},
  URN =		{urn:nbn:de:0030-drops-264326},
  doi =		{10.4230/LIPIcs.ICALP.2026.43},
  annote =	{Keywords: coding theory, interleaved codes, Reed-Solomon codes, semi-random models, unique decoding}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.43
Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio

Authors: Zeyu Guo, Chaoping Xing, Chen Yuan, and Zihan Zhang

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In this paper, we show that random Gabidulin codes of block length n and rate R achieve the (average-radius) list decoding capacity of radius 1-R-ε in the rank metric with an order-optimal column-to-row ratio of O(ε). This extends the recent work of Guo, Xing, Yuan, and Zhang (FOCS 2024), improving their column-to-row ratio from O(ε/n) to O(ε). For completeness, we also establish a matching lower bound on the column-to-row ratio for capacity-achieving Gabidulin codes in the rank metric. Our proof techniques build on the work of Guo and Zhang (FOCS 2023), who showed that randomly punctured Reed-Solomon codes over fields of quadratic size attain the generalized Singleton bound of Shangguan and Tamo (STOC 2020) in the Hamming metric. The proof of our lower bound follows the method of Alrabiah, Guruswami, and Li (SODA 2024) for codes in the Hamming metric.
Cite as

Zeyu Guo, Chaoping Xing, Chen Yuan, and Zihan Zhang. Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 43:1-43:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guo_et_al:LIPIcs.APPROX/RANDOM.2025.43,
  author =	{Guo, Zeyu and Xing, Chaoping and Yuan, Chen and Zhang, Zihan},
  title =	{{Gabidulin Codes Achieve List Decoding Capacity with an Order-Optimal Column-To-Row Ratio}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{43:1--43:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.43},
  URN =		{urn:nbn:de:0030-drops-244095},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.43},
  annote =	{Keywords: coding theory, error-correcting codes, Gabidulin codes, rank-metric codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.54
Decay of Correlation for Edge Colorings When q > 3Δ

Authors: Zejia Chen, Yulin Wang, Chihao Zhang, and Zihan Zhang

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

Abstract
We examine various perspectives on the decay of correlation for the uniform distribution over proper q-edge colorings of graphs with maximum degree Δ. First, we establish the coupling independence property when q ≥ 3Δ for general graphs. Together with the recent work of Chen, Feng, Guo, Zhang and Zou (2024), this result implies a fully polynomial-time approximation scheme (FPTAS) for counting the number of proper q-edge colorings. Next, we prove the strong spatial mixing property on trees, provided that q > (3+o(1))Δ. The strong spatial mixing property is derived from the spectral independence property of a version of the weighted edge coloring distribution, which is established using the matrix trickle-down method developed in Abdolazimi, Liu and Oveis Gharan (FOCS, 2021) and Wang, Zhang and Zhang (STOC, 2024). Finally, we show that the weak spatial mixing property holds on trees with maximum degree Δ if and only if q ≥ 2Δ-1.
Cite as

Zejia Chen, Yulin Wang, Chihao Zhang, and Zihan Zhang. Decay of Correlation for Edge Colorings When q > 3Δ. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 54:1-54:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.54,
  author =	{Chen, Zejia and Wang, Yulin and Zhang, Chihao and Zhang, Zihan},
  title =	{{Decay of Correlation for Edge Colorings When q \rangle 3\Delta}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{54:1--54:18},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-234314},
  doi =		{10.4230/LIPIcs.ICALP.2025.54},
  annote =	{Keywords: Strong Spatial Mixing, Edge Coloring, Approximate Counting}
}
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}
}
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