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Distributed Hypothesis Testing over a Noisy Channel: Error-Exponents Trade-Off.

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This study explores distributed hypothesis testing over noisy channels. A joint coding scheme offers a tighter error-exponent trade-off than separation-based methods for optimal decision-making.

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distributed hypothesis testingerror-exponentshybrid codingjoint source-channel codingnoisy channelsource-channel separation

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Area of Science:

  • Information Theory
  • Statistical Inference
  • Communication Systems

Background:

  • Distributed binary hypothesis testing involves two terminals with independent samples.
  • Communication occurs over a discrete memoryless channel, introducing noise.
  • The decision maker uses local samples and received information for hypothesis testing.

Purpose of the Study:

  • Investigate the trade-off between type I and type II error exponents in distributed hypothesis testing.
  • Develop and compare different coding schemes for this problem.
  • Analyze the performance of separation-based and joint coding schemes.

Main Methods:

  • Utilized a two-terminal distributed binary hypothesis testing framework.
  • Developed a separation-based scheme with type-based compression and unequal error-protection channel coding.
  • Developed a joint scheme incorporating type-based hybrid coding.

Main Results:

  • Derived two inner bounds for the error-exponent trade-off.
  • The separation-based scheme recovers known bounds for special cases.
  • The joint scheme achieves a strictly tighter bound than the separation-based scheme in certain scenarios.

Conclusions:

  • The joint coding scheme provides superior performance for distributed hypothesis testing over noisy channels.
  • This research advances understanding of error-exponent trade-offs in communication systems.
  • The findings have implications for designing efficient distributed decision-making systems.