LIPIcs.APPROX-RANDOM.2024.65.pdf
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Capacity-Achieving Gray Codes
Authors
Venkatesan Guruswami 
,
Hsin-Po Wang
-
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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
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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
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
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References
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