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A New Lower Bound for Noisy Permutation Channels via Divergence Packing.

Lugaoze Feng1, Guocheng Lv1, Xunan Li2

  • 1State Key Laboratory of Photonics and Communications, Peking University, Beijing 100871, China.

Entropy (Basel, Switzerland)
|November 26, 2025
PubMed
Summary

Researchers developed tighter bounds for noisy permutation channels used in biological storage and communication networks. This advancement improves channel coding lower bounds and offers a simpler Gaussian approximation for complex calculations.

Keywords:
divergence packingfinite blocklengthnoisy permutation channelϵ-packing

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Area of Science:

  • Information Theory
  • Coding Theory
  • Applied Mathematics

Background:

  • Noisy permutation channels are crucial for modeling biological storage and communication systems.
  • Existing achievability bounds for these channels require improvement for practical applications.

Purpose of the Study:

  • To derive new, tighter achievability bounds for noisy permutation channels with specific matrix properties.
  • To provide an analytical expression for the achievable code size and explore computational approximations.

Main Methods:

  • Utilized ϵ-packing with Kullback-Leibler divergence as a distance metric.
  • Introduced a novel method to visualize the overlap of error events.
  • Derived an analytical bound involving the channel matrix rank and a new 'channel volume ratio' characteristic.

Main Results:

  • Established new, tighter achievability bounds for noisy permutation channels.
  • The new bound is analytically expressed as log(code size) ≈ ℓlogn - Φ⁻¹(ϵ/G) + logV(W).
  • Numerical results demonstrate significant improvement over existing lower bounds for channel coding.

Conclusions:

  • The novel achievability bound offers a substantial enhancement for channel coding performance.
  • A Gaussian approximation provides a computationally efficient alternative for complex calculations.
  • The findings are applicable to systems employing noisy permutation channels, including biological storage and communication networks.