Found 3 Possible Name Variants:

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**Published in:** LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob.
In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).

Nicolas Resch and Chen Yuan. Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 1:1-1:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{resch_et_al:LIPIcs.ITC.2023.1, author = {Resch, Nicolas and Yuan, Chen}, title = {{Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {1:1--1:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.1}, URN = {urn:nbn:de:0030-drops-183297}, doi = {10.4230/LIPIcs.ITC.2023.1}, annote = {Keywords: Secure transmission, Information theoretical secure, MDS codes} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Despite numerous results about the list decoding of Hamming-metric codes, development of list decoding on rank-metric codes is not as rapid as its counterpart. The bound of list decoding obeys the Gilbert-Varshamov bound in both the metrics. In the case of the Hamming-metric, the Gilbert-Varshamov bound is a trade-off among rate, decoding radius and alphabet size, while in the case of the rank-metric, the Gilbert-Varshamov bound is a trade-off among rate, decoding radius and column-to-row ratio (i.e., the ratio between the numbers of columns and rows). Hence, alphabet size and column-to-row ratio play a similar role for list decodability in each metric. In the case of the Hamming-metric, it is more challenging to list decode codes over smaller alphabets. In contrast, in the case of the rank-metric, it is more difficult to list decode codes with large column-to-row ratio. In particular, it is extremely difficult to list decode square matrix rank-metric codes (i.e., the column-to-row ratio is equal to 1).
The main purpose of this paper is to explicitly construct a class of rank-metric codes 𝒞 of rate R with the column-to-row ratio up to 2/3 and efficiently list decode these codes with decoding radius beyond the decoding radius (1-R)/2 (note that (1-R)/2 is at least half of relative minimum distance δ). In literature, the largest column-to-row ratio of rank-metric codes that can be efficiently list decoded beyond half of minimum distance is 1/2. Thus, it is greatly desired to efficiently design list decoding algorithms for rank-metric codes with the column-to-row ratio bigger than 1/2 or even close to 1. Our key idea is to compress an element of the field F_qⁿ into a smaller F_q-subspace via a linearized polynomial. Thus, the column-to-row ratio gets increased at the price of reducing the code rate. Our result shows that the compression technique is powerful and it has not been employed in the topic of list decoding of both the Hamming and rank metrics. Apart from the above algebraic technique, we follow some standard techniques to prune down the list. The algebraic idea enables us to pin down the message into a structured subspace of dimension linear in the number n of columns. This "periodic" structure allows us to pre-encode the message to prune down the list.

Shu Liu, Chaoping Xing, and Chen Yuan. List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 89:1-89:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{liu_et_al:LIPIcs.ICALP.2023.89, author = {Liu, Shu and Xing, Chaoping and Yuan, Chen}, title = {{List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {89:1--89:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel 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.2023.89}, URN = {urn:nbn:de:0030-drops-181416}, doi = {10.4230/LIPIcs.ICALP.2023.89}, annote = {Keywords: Coding theory, List-decoding, Rank-metric codes} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

In this work we consider the list-decodability and list-recoverability of arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable if every radius pn Hamming ball contains less than L codewords; (p,𝓁,L)_q-list-recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length 𝓁 and again stipulate that there be less than L codewords.
Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate (p,𝓁,L)_q-list-recoverable codes, the quantity we call the zero-rate threshold. Denoting this value by p_*, we in fact show that codes correcting a p_*+ε fraction of errors must have size O_ε(1), i.e., independent of n. Such a result is typically referred to as a "Plotkin bound." To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p_*-ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery.
Technically, proving the Plotkin bound boils down to demonstrating the Schur convexity of a certain function defined on the q-simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q-ary list-decoding; however, we point out that this earlier proof is flawed.

Nicolas Resch, Chen Yuan, and Yihan Zhang. Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 99:1-99:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{resch_et_al:LIPIcs.ICALP.2023.99, author = {Resch, Nicolas and Yuan, Chen and Zhang, Yihan}, title = {{Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {99:1--99:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel 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.2023.99}, URN = {urn:nbn:de:0030-drops-181518}, doi = {10.4230/LIPIcs.ICALP.2023.99}, annote = {Keywords: Coding theory, List-decoding, List-recovery, Zero-rate thresholds} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

In this work, we prove new results concerning the combinatorial properties of random linear codes. By applying the thresholds framework from Mosheiff et al. (FOCS 2020) we derive fine-grained results concerning the list-decodability and -recoverability of random linear codes.
Firstly, we prove a lower bound on the list-size required for random linear codes over 𝔽_q ε-close to capacity to list-recover with error radius ρ and input lists of size 𝓁. We show that the list-size L must be at least {log_q binom{q,𝓁}}-R}/ε, where R is the rate of the random linear code. This is analogous to a lower bound for list-decoding that was recently obtained by Guruswami et al. (IEEE TIT 2021B). As a comparison, we also pin down the list size of random codes which is {log_q binom{q,𝓁}}/ε. This result almost closes the O({q log L}/L) gap left by Guruswami et al. (IEEE TIT 2021A). This leaves open the possibility (that we consider likely) that random linear codes perform better than the random codes for list-recoverability, which is in contrast to a recent gap shown for the case of list-recovery from erasures (Guruswami et al., IEEE TIT 2021B).
Next, we consider list-decoding with constant list-sizes. Specifically, we obtain new lower bounds on the rate required for:
- List-of-3 decodability of random linear codes over 𝔽₂;
- List-of-2 decodability of random linear codes over 𝔽_q (for any q). This expands upon Guruswami et al. (IEEE TIT 2021A) which only studied list-of-2 decodability of random linear codes over 𝔽₂. Further, in both cases we are able to show that the rate is larger than that which is possible for uniformly random codes.
A conclusion that we draw from our work is that, for many combinatorial properties of interest, random linear codes actually perform better than uniformly random codes, in contrast to the apparently standard intuition that uniformly random codes are best.

Nicolas Resch and Chen Yuan. Threshold Rates of Code Ensembles: Linear Is Best. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 104:1-104:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{resch_et_al:LIPIcs.ICALP.2022.104, author = {Resch, Nicolas and Yuan, Chen}, title = {{Threshold Rates of Code Ensembles: Linear Is Best}}, booktitle = {49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)}, pages = {104:1--104:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-235-8}, ISSN = {1868-8969}, year = {2022}, volume = {229}, editor = {Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.104}, URN = {urn:nbn:de:0030-drops-164456}, doi = {10.4230/LIPIcs.ICALP.2022.104}, annote = {Keywords: Random Linear Codes, List-Decoding, List-Recovery, Threshold Rates} }

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Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Locally recoverable codes are a class of block codes with an additional property called locality. A locally recoverable code with locality r can recover a symbol by reading at most r other symbols. Recently, it was discovered by several authors that a q-ary optimal locally recoverable code, i.e., a locally recoverable code achieving the Singleton-type bound, can have length much bigger than q+1. In this paper, we present both the upper bound and the lower bound on the length of optimal locally recoverable codes. Our lower bound improves the best known result in [Yuan Luo et al., 2018] for all distance d >= 7. This result is built on the observation of the parity-check matrix equipped with the Vandermonde structure. It turns out that a parity-check matrix with the Vandermonde structure produces an optimal locally recoverable code if it satisfies a certain expansion property for subsets of F_q. To our surprise, this expansion property is then shown to be equivalent to a well-studied problem in extremal graph theory. Our upper bound is derived by an refined analysis of the arguments of Theorem 3.3 in [Venkatesan Guruswami et al., 2018].

Chaoping Xing and Chen Yuan. Construction of Optimal Locally Recoverable Codes and Connection with Hypergraph. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 98:1-98:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{xing_et_al:LIPIcs.ICALP.2019.98, author = {Xing, Chaoping and Yuan, Chen}, title = {{Construction of Optimal Locally Recoverable Codes and Connection with Hypergraph}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {98:1--98:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.98}, URN = {urn:nbn:de:0030-drops-106745}, doi = {10.4230/LIPIcs.ICALP.2019.98}, annote = {Keywords: Locally Repairable Codes, Hypergraph} }

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**Published in:** LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

A locally repairable code (LRC) with locality r allows for the recovery of any erased codeword symbol using only r other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of LRCs - an LRC attaining this trade-off is deemed optimal. Such optimal LRCs have been constructed over alphabets growing linearly in the block length. Unlike the classical Singleton bound, however, it was not known if such a linear growth in the alphabet size is necessary, or for that matter even if the alphabet needs to grow at all with the block length. Indeed, for small code distances 3,4, arbitrarily long optimal LRCs were known over fixed alphabets.
Here, we prove that for distances d >=slant 5, the code length n of an optimal LRC over an alphabet of size q must be at most roughly O(d q^3). For the case d=5, our upper bound is O(q^2). We complement these bounds by showing the existence of optimal LRCs of length Omega_{d,r}(q^{1+1/floor[(d-3)/2]}) when d <=slant r+2. Our bounds match when d=5, pinning down n=Theta(q^2) as the asymptotically largest length of an optimal LRC for this case.

Venkatesan Guruswami, Chaoping Xing, and Chen Yuan. How Long Can Optimal Locally Repairable Codes Be?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 41:1-41:11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX-RANDOM.2018.41, author = {Guruswami, Venkatesan and Xing, Chaoping and Yuan, Chen}, title = {{How Long Can Optimal Locally Repairable Codes Be?}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)}, pages = {41:1--41:11}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-085-9}, ISSN = {1868-8969}, year = {2018}, volume = {116}, editor = {Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.41}, URN = {urn:nbn:de:0030-drops-94458}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2018.41}, annote = {Keywords: Locally Repairable Code, Singleton Bound} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Subspace designs are a (large) collection of high-dimensional subspaces {H_i} of F_q^m such that for any low-dimensional subspace W, only a small number of subspaces from the collection have non-trivial intersection with W; more precisely, the sum of dimensions of W cap H_i is at most some parameter L. The notion was put forth by Guruswami and Xing (STOC'13) with applications to list decoding variants of Reed-Solomon and algebraic-geometric codes, and later also used for explicit rank-metric codes with optimal list decoding radius.
Guruswami and Kopparty (FOCS'13, Combinatorica'16) gave an explicit construction of subspace designs with near-optimal parameters. This construction was based on polynomials and has close connections to folded Reed-Solomon codes, and required large field size (specifically q >= m). Forbes and Guruswami (RANDOM'15) used this construction to give explicit constant degree "dimension expanders" over large fields, and noted that subspace designs are a powerful tool in linear-algebraic pseudorandomness.
Here, we construct subspace designs over any field, at the expense of a modest worsening of the bound $L$ on total intersection dimension. Our approach is based on a (non-trivial) extension of the polynomial-based construction to algebraic function fields, and instantiating the approach with cyclotomic function fields. Plugging in our new subspace designs in the construction of Forbes and Guruswami yields dimension expanders over F^n for any field F, with logarithmic degree and expansion guarantee for subspaces of dimension Omega(n/(log(log(n)))).

Venkatesan Guruswami, Chaoping Xing, and Chen Yuan. Subspace Designs Based on Algebraic Function Fields. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 86:1-86:10, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guruswami_et_al:LIPIcs.ICALP.2017.86, author = {Guruswami, Venkatesan and Xing, Chaoping and Yuan, Chen}, title = {{Subspace Designs Based on Algebraic Function Fields}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {86:1--86:10}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.86}, URN = {urn:nbn:de:0030-drops-73712}, doi = {10.4230/LIPIcs.ICALP.2017.86}, annote = {Keywords: Subspace Design, Dimension Expander, List Decoding} }

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**Published in:** LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Molecular programming - a paradigm wherein molecules are engineered to perform computation - shows great potential for applications in nanotechnology, disease diagnostics and smart therapeutics. A key challenge is to identify systematic approaches for compiling abstract models of computation to molecules. Due to their wide applicability, one of the most useful abstractions to realize is neural networks. In prior work, real-valued weights were achieved by individually controlling the concentrations of the corresponding "weight" molecules. However, large-scale preparation of reactants with precise concentrations quickly becomes intractable. Here, we propose to bypass this fundamental problem using Binarized Neural Networks (BNNs), a model that is highly scalable in a molecular setting due to the small number of distinct weight values. We devise a noise-tolerant digital molecular circuit that compactly implements a majority voting operation on binary-valued inputs to compute the neuron output. The network is also rate-independent, meaning the speed at which individual reactions occur does not affect the computation, further increasing robustness to noise. We first demonstrate our design on the MNIST classification task by simulating the system as idealized chemical reactions. Next, we map the reactions to DNA strand displacement cascades, providing simulation results that demonstrate the practical feasibility of our approach. We perform extensive noise tolerance simulations, showing that digital molecular neurons are notably more robust to noise in the concentrations of chemical reactants compared to their analog counterparts. Finally, we provide initial experimental results of a single binarized neuron. Our work suggests a solid framework for building even more complex neural network computation.

Johannes Linder, Yuan-Jyue Chen, David Wong, Georg Seelig, Luis Ceze, and Karin Strauss. Robust Digital Molecular Design of Binarized Neural Networks. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 1:1-1:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{linder_et_al:LIPIcs.DNA.27.1, author = {Linder, Johannes and Chen, Yuan-Jyue and Wong, David and Seelig, Georg and Ceze, Luis and Strauss, Karin}, title = {{Robust Digital Molecular Design of Binarized Neural Networks}}, booktitle = {27th International Conference on DNA Computing and Molecular Programming (DNA 27)}, pages = {1:1--1:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-205-1}, ISSN = {1868-8969}, year = {2021}, volume = {205}, editor = {Lakin, Matthew R. and \v{S}ulc, Petr}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.1}, URN = {urn:nbn:de:0030-drops-146685}, doi = {10.4230/LIPIcs.DNA.27.1}, annote = {Keywords: Molecular Computing, Neural Network, Binarized Neural Network, Digital Logic, DNA, Strand Displacement} }

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**Published in:** LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Byzantine agreement (BA) is a distributed consensus problem where n processors want to reach agreement on an 𝓁-bit message or value, but up to t of the processors are dishonest or faulty. The challenge of this BA problem lies in achieving agreement despite the presence of dishonest processors who may arbitrarily deviate from the designed protocol. In this work by using coding theory, together with graph theory and linear algebra, we design a coded BA protocol (termed as COOL) that achieves consensus on an 𝓁-bit message with optimal resilience, asymptotically optimal round complexity, and asymptotically optimal communication complexity when 𝓁 ≥ t log t, simultaneously. The proposed COOL is a deterministic BA protocol that is guaranteed to be correct in all executions (error free) and does not rely on cryptographic technique such as signatures, hashing, authentication and secret sharing (signature free). It is secure against computationally unbounded adversary who takes full control over the dishonest processors (information-theoretic secure). The main idea of the proposed COOL is to use a carefully-crafted error correction code that provides an efficient way of exchanging "compressed" information among distributed nodes, while keeping the ability of detecting errors, masking errors, and making a consistent and validated agreement at honest distributed nodes. We show that our results can also be extended to the setting of Byzantine broadcast, aka Byzantine generals problem, where the honest processors want to agree on the message sent by a leader who is potentially dishonest. The results reveal that coding is an effective approach for achieving the fundamental limits of Byzantine agreement and its variants. Our protocol analysis borrows tools from coding theory, graph theory and linear algebra.

Jinyuan Chen. Optimal Error-Free Multi-Valued Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 17:1-17:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen:LIPIcs.DISC.2021.17, author = {Chen, Jinyuan}, title = {{Optimal Error-Free Multi-Valued Byzantine Agreement}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {17:1--17:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-210-5}, ISSN = {1868-8969}, year = {2021}, volume = {209}, editor = {Gilbert, Seth}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.17}, URN = {urn:nbn:de:0030-drops-148190}, doi = {10.4230/LIPIcs.DISC.2021.17}, annote = {Keywords: Byzantine agreement, information-theoretic security, error correction codes} }

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