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Summary
This summary is machine-generated.

This study introduces private compression methods to minimize encoded message length while protecting private data from adversaries. It explores perfect and non-perfect privacy scenarios, developing new bounds and coding techniques for enhanced data security.

Keywords:
extended functional representation lemmalossless compressionminimum entropy couplingprivate variable-length codingseparation technique

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Area of Science:

  • Information Theory
  • Data Compression
  • Cybersecurity

Background:

  • Addresses private compression where data Y is correlated with private attribute X.
  • Encoder uses a private compression mechanism to create an encoded message C.
  • An adversary attempts to estimate X from the encoded message C.

Purpose of the Study:

  • To design an encoded message C with minimum average length under privacy constraints.
  • To investigate scenarios with zero (perfect) and non-zero (non-perfect) privacy leakage.
  • To improve existing bounds on data compression with privacy.

Main Methods:

  • Linear programming to find upper bounds on optimizer entropy for perfect privacy.
  • Two-part construction coding for achieving upper bounds in specific cases.
  • Minimum entropy coupling and greedy entropy-based algorithms to strengthen bounds.
  • Analysis of upper and lower bounds using different privacy metrics for non-perfect privacy.

Main Results:

  • Strengthened existing bounds for private compression, particularly when |X|≥|Y| or for specific joint distributions.
  • Achieved upper bounds using two-part construction coding, improving upon prior results.
  • Derived and analyzed bounds for non-perfect privacy scenarios, demonstrating asymptotic tightness in examples.

Conclusions:

  • Developed novel private compression techniques balancing data compression efficiency and privacy.
  • Established new theoretical bounds and practical coding strategies for secure data transmission.
  • The proposed methods offer improved performance over existing approaches for private information retrieval.