Foto von Ilya Vorobyev

Ilya Vorobyev

Technische Universität München

Lehrstuhl für Nachrichtentechnik (Prof. Kramer)

Postadresse

Postal:
Theresienstr. 90
80333 München

Biography

Ilya Vorobyev received the M.Sc. and Ph.D. degrees in mathematics from Lomonosov Moscow State University in 2013 and 2017, respectively. From 2015 to 2017, he was a Research Engineer at the Huawei Research and Development Department, Moscow. He was also a Researcher at the Institute for Information Transmission Problems from 2015 to 2017. From 2017 to 2019, he has been a Senior Researcher at the Advanced Combinatorics and Complex Networks Laboratory, Moscow Institute of Physics and Technology. From 2018 to 2022, he has also been a Research Scientist at the Center for Computational and Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology. His research interests are combinatorics and coding theory.

Laufende Abschlussarbeiten

Sizes of balls in fixed length Levenstein metric

Stichworte:
Levenstein's distance, insertion/deletion

Beschreibung

The size of the ball of radius d in Levenstein metric depends on the center of the ball. During this project it is suggested to investigate the distribution of the sizes of Levenstein balls, i.e. estimate the mathematical expectation and variance of the size, and find its maximal and minimum value.

For the case d=1 and 2 this question have already been addressed in papers [1] and [2] correspondingly, where some theoretical results have been obtained. The task of the project is to verify it with numerical computation, and obtain similar estimations for d>2.

 

[1] Bar-Lev, D., Etzion, T., & Yaakobi, E. (2021, July). On Levenshtein balls with radius one. In 2021 IEEE International Symposium on Information Theory (ISIT) (pp. 1979-1984). IEEE.

[2] He, L., & Ye, M. (2023, June). The size of Levenshtein ball with radius 2: Expectation and concentration bound. In 2023 IEEE International Symposium on Information Theory (ISIT) (pp. 850-855). IEEE.

Betreuer:

Correcting 2 errors in binary channels with feedback

Beschreibung

In paper 

"Correcting a Single Error in Feedback Channels" the problem of correcting a single error with feedback was investigated. It was mainly devoted to binary channels, namely, binary symmetric and asymmetric channels. A general theorem, which allows constructing codes correcting one error with one feedback, was proved. For the symmetric channel with one error, it was proved that with two feedbacks one can transmit as many messages as with complete feedback.

In this project, it is proposed to generalize these results to the case of two errors. Namely, it is required to prove the theorem, which describes optimal codes, correcting 2 errors with one feedback. After that, some optimization problems should be solved to find the parameters of optimal codes.

Betreuer:

Publications

2023

  • Akhmejanova, Margarita; Olmezov, Konstantin; Volostnov, Aleksei; Vorobyev, Ilya; Vorob’ev, Konstantin; Yarovikov, Yury: Wiener index and graphs, almost half of whose vertices satisfy Šoltés property. Discrete Applied Mathematics 325, 2023, 37-42 mehr… Volltext ( DOI )
  • Goshkoder, Daniil; Polyanskii, Nikita; Vorobyev, Ilya: Codes Correcting a Single Long Duplication Error. 2023 IEEE International Symposium on Information Theory (ISIT), IEEE, 2023 mehr… Volltext ( DOI )
  • Gu, Yujie; Vorobyev, Ilya; Miao, Ying: Secure Codes with List Decoding. IEEE Transactions on Information Theory, 2023, 1-1 mehr… Volltext ( DOI )
  • Vorobyev, Ilya; Lebedev, Vladimir; Lebedev, Alexey: Correcting One Error in Non-Binary Channels with Feedback. 2023 IEEE International Symposium on Information Theory (ISIT), IEEE, 2023 mehr… Volltext ( DOI )

2022

  • Gu, Yujie; Vorobyev, Ilya; Miao, Ying: Secure codes with list decoding. 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, 2022 mehr… Volltext ( DOI )
  • Vorobyev, I. V.; Deppe, C.; Lebedev, A. V.; Lebedev, V. S.: Correcting a Single Error in Feedback Channels. Problems of Information Transmission 58 (4), 2022, 329-340 mehr… Volltext ( DOI )
  • Vorobyev, Ilya: Complete traceability multimedia fingerprinting codes resistant to averaging attack and adversarial noise with optimal rate. Designs, Codes and Cryptography, 2022 mehr… Volltext ( DOI )
  • Vorob’ev, I. V.; Lebedev, V. S.: Improved Upper Bounds for the Rate of Separating and Completely Separating Codes. Problems of Information Transmission 58 (3), 2022, 242-253 mehr… Volltext ( DOI )

2021

  • Bitar, Rawad; Hanna, Serge Kas; Polyanskii, Nikita; Vorobyev, Ilya: Optimal Codes Correcting Localized Deletions. 2021 IEEE International Symposium on Information Theory (ISIT), IEEE, 2021 mehr… Volltext ( DOI )
  • Holzbaur, Lukas; Polyanskaya, Rina; Polyanskii, Nikita; Vorobyev, Ilya; Yaakobi, Eitan: Lifted Reed-Solomon Codes and Lifted Multiplicity Codes. IEEE Transactions on Information Theory 67 (12), 2021, 8051--8069 mehr… Volltext ( DOI )
  • Holzbaur, Lukas; Polyanskaya, Rina; Polyanskii, Nikita; Vorobyev, Ilya; Yaakobi, Eitan: On Lifted Multiplicity Codes. 2020 IEEE Information Theory Workshop (ITW), IEEE, 2021 mehr… Volltext ( DOI )
  • Liu, Hedongliang; Polianskii, Nikita; Vorobyev, Ilya; Wachter-Zeh, Antonia: Almost affinely disjoint subspaces. Finite Fields and Their Applications 75, 2021, 101879 mehr… Volltext ( DOI )
  • Maringer, G.; Polyanskii, N. A.; Vorobyev, I. V.; Welter, L.: Feedback Insertion-Deletion Codes. Problems of Information Transmission 57 (3), 2021, 212-240 mehr… Volltext ( DOI )
  • Maringer, Georg; Polyanskii, Nikita; Vorobyev, Ilya; Welter, Lorenz: Feedback Insertion-Deletion Codes. 2020 IEEE Information Theory Workshop (ITW), IEEE, 2021 mehr… Volltext ( DOI )
  • Vorobyev, Ilya: Fast Decoding of Union-Free Codes. 2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY), IEEE, 2021 mehr… Volltext ( DOI )

2020

  • Holzbaur, Lukas; Polyanskaya, Rina; Polyanskii, Nikita; Vorobyev, Ilya: Lifted Reed-Solomon Codes with Application to Batch Codes. 2020 IEEE International Symposium on Information Theory (ISIT), IEEE, 2020 mehr… Volltext ( DOI )
  • Polyanskaya, Rina; Polyanskii, Nikita; Vorobyev, Ilya: Binary Batch Codes With Improved Redundancy. IEEE Transactions on Information Theory 66 (12), 2020, 7360--7370 mehr… Volltext ( DOI )
  • Polyanskii, Nikita; Vorobyev, Ilya: Duplication with transposition distance to the root for q-ary strings. 2020 IEEE International Symposium on Information Theory (ISIT), IEEE, 2020 mehr… Volltext ( DOI )
  • Vorobyev, Ilya: Optimal Multistage Group Testing Algorithm for 3 Defectives. 2020 IEEE International Symposium on Information Theory (ISIT), IEEE, 2020 mehr… Volltext ( DOI )

2019

  • D′yachkov, Arkadii; Polyanskii, Nikita; Shchukin, Vladislav; Vorobyev, Ilya: Separable Codes for the Symmetric Multiple-Access Channel. IEEE Transactions on Information Theory 65 (6), 2019, 3738--3750 mehr… Volltext ( DOI )
  • D′yachkov, Arkadii; Polyanskii, Nikita; Shchukin, Vladislav; Vorobyev, Ilya: Hypothesis Test for Bounds on the Size of Random Defective Set. IEEE Transactions on Signal Processing 67 (22), 2019, 5775--5784 mehr… Volltext ( DOI )
  • Egorova, Elena; Vorobyev, Ilya: New lower bound on the rate of traceability set systems. 2019 XVI International Symposium" Problems of Redundancy in Information and Control Systems"(REDUNDANCY), 2019 mehr…
  • Jiang, Zilin; Polyanskii, Nikita; Vorobyev, Ilya: On Capacities of the Two-User Union Channel With Complete Feedback. IEEE Transactions on Information Theory 65 (5), 2019, 2774--2781 mehr… Volltext ( DOI )
  • Polyanskii, Nikita; Vorobyev, Ilya: Constructions of batch codes via finite geometry. 2019 IEEE International Symposium on Information Theory (ISIT), 2019 mehr…
  • Polyanskii, Nikita; Vorobyev, Ilya: Trivariate lifted codes with disjoint repair groups. 2019 XVI International Symposium" Problems of Redundancy in Information and Control Systems"(REDUNDANCY), 2019 mehr…
  • Vorobyev, Ilya: A new algorithm for two-stage group testing. 2019 IEEE International Symposium on Information Theory (ISIT), 2019 mehr…
  • Vorobyev, Ilya; Usatyuk, Vasiliy;: Construction of High Performance Block and Convolutional Multi-Edge Type QC-LDPC codes. 2019 42nd International Conference on Telecommunications and Signal Processing (TSP), 2019 mehr… Volltext ( DOI )

2018

  • D′yachkov, Arkadii; Polyanskii, Nikita; Shchukin, Vladislav; Vorobyev, Ilya: Separable Codes for the Symmetric Multiple-Access Channel. 2018 IEEE International Symposium on Information Theory (ISIT), 2018 mehr… Volltext ( DOI )
  • Usatyuk, Vasiliy; Vorobyev, Ilya: Simulated Annealing Method for Construction of High-Girth QC-LDPC Codes. 2018 41st International Conference on Telecommunications and Signal Processing (TSP), 2018 mehr…
  • Vorobyev, Ilya; Polyanskii, Nikita; Svistunov, German; Egorov, Sergey; Usatyuk, Vasiliy: Generalization of Floor Lifting for QC-LDPC Codes: Theoretical Properties and Applications. 2018 IEEE East-West Design & Test Symposium (EWDTS), 2018 mehr…

2017

  • D'yachkov, A.; Vorobyev, I.; Polyanskii, N.; Shchukin, V.: Almost cover-free codes and designs. Designs, Codes, and Cryptography 82 (1-2), 2017, 231-247 mehr…
  • D'yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Y.: Cover-free codes and separating system codes. Designs, Codes, and Cryptography 82 (1-2), 2017, 197-209 mehr…
  • D'yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Y.: Symmetric disjunctive list-decoding codes. Designs, Codes, and Cryptography 82 (1-2), 2017, 211-229 mehr…
  • D′yachkov, A.; Vorobyev, I.; Polyanskii, N.; Shchukin, V.: Hypothesis test for upper bound on the size of random defective set. IEEE International Symposium on Information Theory - Proceedings, 2017, 978-982 mehr…
  • Vorobyev, I.V.: Bounds on the rate of separating codes. Problems of Information Transmission 53 (1), 2017, 30-41 mehr…

2016

  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Yu.: On a hypergraph approach to multistage group testing problems. IEEE International Symposium on Information Theory - Proceedings 2016-August, 2016, 1183-1191 mehr…
  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Yu.: On multistage learning a hidden hypergraph. IEEE International Symposium on Information Theory - Proceedings 2016-August, 2016, 1178-1182 mehr…

2015

  • D'yachkov, A.G.; Vorobyev, I.V.; Polyansky, N.A.; Shchukin, V.Y.: Almost disjunctive list-decoding codes. Problems of Information Transmission 51 (2), 2015, 110-131 mehr…
  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Y.: Almost cover-free codes and designs. IEEE International Symposium on Information Theory - Proceedings 2015-June, 2015, 2899-2903 mehr…
  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Y.: Cover-free codes and separating system codes. IEEE International Symposium on Information Theory - Proceedings 2015-June, 2015, 2894-2898 mehr…
  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Y.: Symmetric disjunctive list-decoding codes. IEEE International Symposium on Information Theory - Proceedings 2015-June, 2015, 2236-2240 mehr…

2014

  • D′yachkov, A.G.; Vorobyev, I.V.; Polyanskii, N.A.; Shchukin, V.Yu.: Bounds on the rate of superimposed codes. IEEE International Symposium on Information Theory - Proceedings, 2014, 2341-2345 mehr…
  • D′yachkov, A.G.; Vorobyev, I.V.; Polyansky, N.A.; Shchukin, V.Y.: Bounds on the rate of disjunctive codes. Problems of Information Transmission 50 (1), 2014, 27-56 mehr…