LIPIcs.APPROX-RANDOM.2024.65.pdf
- Filesize: 0.68 MB
- 9 pages
Document
Capacity-Achieving Gray Codes
Authors
Venkatesan Guruswami 
,
Hsin-Po Wang
-
Part of:
Volume:
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-16
File
Document Identifiers
Author Details
Cite AsGet BibTex
Venkatesan Guruswami and Hsin-Po Wang. Capacity-Achieving Gray Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 65:1-65:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.65
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.65
Abstract
To ensure differential privacy, one can reveal an integer fuzzily in two ways: (a) add some Laplace noise to the integer, or (b) encode the integer as a binary string and add iid BSC noise. The former is simple and natural while the latter is flexible and affordable, especially when one wants to reveal a sparse vector of integers. In this paper, we propose an implementation of (b) that achieves the capacity of the BSC with positive error exponents. Our implementation adds error-correcting functionality to Gray codes by mimicking how software updates back up the files that are getting updated ("coded Gray code"). In contrast, the old implementation of (b) interpolates between codewords of a black-box error-correcting code ("Grayed code").
Subject Classification
ACM Subject Classification
- Mathematics of computing → Coding theory
- Security and privacy → Privacy-preserving protocols
Keywords
- Gray codes
- capacity-achieving codes
- differential privacy
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
- Martin Aumüller, Christian Janos Lebeda, and Rasmus Pagh. Representing Sparse Vectors with Differential Privacy, Low Error, Optimal Space, and Fast Access. Journal of Privacy and Confidentiality, 12(2), November 2022. URL: https://doi.org/10.29012/jpc.809.
- Roni Con, Dorsa Fathollahi, Ryan Gabrys, Mary Wootters, and Eitan Yaakobi. Robust gray codes approaching the optimal rate, 2024. URL: https://arxiv.org/abs/2406.17689.
- Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith. Calibrating Noise to Sensitivity in Private Data Analysis. Journal of Privacy and Confidentiality, 7(3):17-51, 2016. URL: https://doi.org/10.29012/jpc.v7i3.405.
- Dorsa Fathollahi and Mary Wootters. Improved construction of robust gray code, 2024. URL: https://arxiv.org/abs/2401.15291.
- Venkatesan Guruswami and Piotr Indyk. Linear-Time Encodable/Decodable Codes With Near-Optimal Rate. IEEE Transactions on Information Theory, 51(10):3393-3400, October 2005. URL: https://doi.org/10.1109/TIT.2005.855587.
- David Rasmussen Lolck and Rasmus Pagh. Shannon meets Gray: Noise-robust, Low-sensitivity Codes with Applications in Differential Privacy. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Proceedings, pages 1050-1066. Society for Industrial and Applied Mathematics, January 2024. URL: https://doi.org/10.1137/1.9781611977912.40.
- OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences, 2024. Published electronically at URL: http://oeis.org.