Differential Privacy over Hamming Codes

2026-06-26

AI Summary

This work addresses the challenge of transmitting count query results over a binary symmetric channel while preserving differential privacy. Conventional mechanisms often require injecting additional noise, which compromises utility or increases error rates. The authors propose an optimal permutation strategy for Hamming code codewords that leverages the channel’s inherent noise to strengthen differential privacy guarantees—without introducing extra perturbation, degrading data utility, or incurring additional computational overhead. By integrating differential privacy with information-theoretic coding principles, the method achieves enhanced privacy-utility trade-offs while maintaining end-to-end decoding accuracy. This approach establishes a novel paradigm for privacy-preserving communication in bandwidth-constrained settings.

Abstract

We consider the transmission of the outputs of counting queries over a binary symmetric channel (BSC), where Hamming codes are employed as the channel encoder. Since the channel is inherently noisy, this transmission already provides a degree of privacy protection ``for free'', albeit at the cost of reduced utility in the form of decoding errors. A natural question is whether this privacy can be further improved (i) without any additional real-time obfuscation of the data, such as injecting artificial noise prior to transmission, and (ii) without increasing the end-to-end error probability. In this work, we answer this question in the affirmative by deriving an optimal codeword arrangement that strictly improves differential privacy guarantees while incurring no real-time computational overhead and no degradation in utility.

Problem

• Differential Privacy
• Hamming Codes
• Binary Symmetric Channel
• Counting Queries
• Privacy-Utility Tradeoff

Innovation

• Differential Privacy
• Hamming Codes
• Binary Symmetric Channel
• Codeword Arrangement
• Privacy-Utility Tradeoff