Coding theory, additive combinatorics and machine learning
Event details
| Date | 16.06.2025 |
| Hour | 14:00 › 16:00 |
| Speaker | Vladyslav Shashkov |
| Location | |
| Category | Conferences - Seminars |
EDIC candidacy exam jury
Exam president: Prof. Rüdiger Urbanke
Thesis advisor: Prof. Emmanuel Abbé
Thesis co-advisor: Prof. Maryna Viazovska
Co-examiner: Prof. Florian Richter
Abstract
An important goal of coding theory is to identify capacity-achieving code families. While Shannon's result proved that random codes achieve capacity, the search of deterministic codes remains open. I contributed to a concise mathematical argument showing that Reed-Muller codes achieve weak Shannon capacity. I aim to address the capacity conjecture for doubly transitive codes using mathematical tools such as Fourier sums, with the goal of advancing our understanding of highly symmetric, capacity-achieving codes.
Selected papers
1. "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels", Erdal Arikan https://arxiv.org/pdf/0807.3917
2. "Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting" Emmanuel Abbé and Colin Sandon, https://arxiv.org/pdf/2312.04329
3. "On a conjecture of Marton", W. T. Gowers, Ben Green, Frederick Manners, and Terence Tao, https://arxiv.org/pdf/2311.05762
Exam president: Prof. Rüdiger Urbanke
Thesis advisor: Prof. Emmanuel Abbé
Thesis co-advisor: Prof. Maryna Viazovska
Co-examiner: Prof. Florian Richter
Abstract
An important goal of coding theory is to identify capacity-achieving code families. While Shannon's result proved that random codes achieve capacity, the search of deterministic codes remains open. I contributed to a concise mathematical argument showing that Reed-Muller codes achieve weak Shannon capacity. I aim to address the capacity conjecture for doubly transitive codes using mathematical tools such as Fourier sums, with the goal of advancing our understanding of highly symmetric, capacity-achieving codes.
Selected papers
1. "Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels", Erdal Arikan https://arxiv.org/pdf/0807.3917
2. "Reed-Muller codes have vanishing bit-error probability below capacity: a simple tighter proof via camellia boosting" Emmanuel Abbé and Colin Sandon, https://arxiv.org/pdf/2312.04329
3. "On a conjecture of Marton", W. T. Gowers, Ben Green, Frederick Manners, and Terence Tao, https://arxiv.org/pdf/2311.05762
Practical information
- General public
- Free