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Area of Science:

  • Information Theory
  • Probability Theory
  • Functional Analysis

Background:

  • The study addresses the Gaussian distortion-rate-perception functions, which are crucial in information theory.
  • Limited common randomness presents a challenge in analyzing these functions under different perception measures.
  • Existing bounds on these functions require a unified framework for assessment.

Purpose of the Study:

  • To establish a constrained version of Talagrand's transportation inequality.
  • To reveal an intrinsic connection between Gaussian distortion-rate-perception functions under Kullback-Leibler divergence and squared Wasserstein-2 distance.
  • To provide a framework for assessing existing bounds and demonstrate their non-redundancy.

Main Methods:

  • Establishing a constrained version of Talagrand's transportation inequality.
  • Analyzing the connection between different perception measures using limited common randomness.
  • Evaluating the non-redundancy of existing bounds through the established framework.

Main Results:

  • A constrained Talagrand's transportation inequality is established.
  • An intrinsic connection is revealed between Gaussian distortion-rate-perception functions under Kullback-Leibler divergence and squared Wasserstein-2 distance.
  • The best-known bounds by Xie et al. are shown to be nonredundant within this new framework.

Conclusions:

  • The established connection offers an organizational framework for understanding distortion-rate-perception functions.
  • The findings clarify the relationship between different divergence measures in information theory.
  • The work validates and refines the assessment of existing theoretical bounds.