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Encoding Individual Source Sequences for the Wiretap Channel.

Neri Merhav1

  • 1The Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 3200003, Israel.

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Summary
This summary is machine-generated.

This study establishes a necessary condition for secure data transmission over degraded wiretap channels using finite-state machines. It also determines the minimum randomness rate required for secure encoding, crucial for data security.

Keywords:
Lempel–Ziv algorithmfinite-state machineindividual sequencephysical layer securitysemantic securityside informationwiretap channel

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Area of Science:

  • Information Theory
  • Coding Theory
  • Cybersecurity

Background:

  • Secure communication over wiretap channels is essential for protecting sensitive data.
  • Finite-state machines offer a practical model for implementing encoders and decoders.
  • Degraded wiretap channels present unique challenges for achieving both reliability and security.

Purpose of the Study:

  • To derive a necessary condition for reliable and secure transmission over degraded wiretap channels.
  • To establish a lower bound on the achievable bandwidth expansion factor.
  • To determine the minimum rate of random bits required for secure encoding.

Main Methods:

  • Analysis of deterministic source sequence encoding for finite-state machine-based wiretap channels.
  • Derivation of converse bounds for bandwidth expansion and randomness rate.
  • Utilizing Lempel-Ziv compression and channel coding for achievability schemes.

Main Results:

  • A necessary condition for reliable and secure transmission is established, providing a lower bound on bandwidth expansion.
  • This bound is shown to be asymptotically achievable.
  • A lower bound on the necessary rate of random bits for secure encoding is derived and achieved.

Conclusions:

  • The findings provide fundamental limits for secure communication system design using finite-state machines.
  • The results are extended to scenarios with side information at the decoder and eavesdropper.
  • The study contributes to the theoretical understanding of secure information transmission under practical constraints.