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Capacity Bounds and Low-Complexity Constellation Shaping under Mixed Gaussian-Impulsive Noise

Tianfu Qi, Jun Wang

TL;DR

This work tackles capacity bounds for channels with memoryless mixed Gaussian-impulsive noise and develops practical constellation shaping methods. By deriving a tight lower bound via the entropy power inequality and a duality-based upper bound, it proves asymptotic convergence of the bounds and provides a closed-form high-power capacity expression. Leveraging the asymptotically optimal input distribution, the authors implement low-complexity geometric and probabilistic shaping that do not require iterative optimization. Simulations show the bounds are extremely tight and the shaped constellations deliver significant mutual-information gains over baseline schemes, validating the practical relevance of the proposed approach.

Abstract

This paper investigates the bounds on channel capacity and constellation shaping under memoryless mixed noise, which is composed of impulsive noise (IN) and white Gaussian noise (WGN). The capacity bounds are derived using the entropy power inequality and the dual expression of capacity. It is then shown that the proposed lower and upper bounds asymptotically converge to the true channel capacity, and the analytic asymptotic capacity expression is obtained. Leveraging this property, we design a low-complexity constellation shaping method that operates without iterative procedures. Simulation results demonstrate that the derived bounds are remarkably tight, and the shaped constellation achieves the highest mutual information among all considered baseline schemes.

Capacity Bounds and Low-Complexity Constellation Shaping under Mixed Gaussian-Impulsive Noise

TL;DR

This work tackles capacity bounds for channels with memoryless mixed Gaussian-impulsive noise and develops practical constellation shaping methods. By deriving a tight lower bound via the entropy power inequality and a duality-based upper bound, it proves asymptotic convergence of the bounds and provides a closed-form high-power capacity expression. Leveraging the asymptotically optimal input distribution, the authors implement low-complexity geometric and probabilistic shaping that do not require iterative optimization. Simulations show the bounds are extremely tight and the shaped constellations deliver significant mutual-information gains over baseline schemes, validating the practical relevance of the proposed approach.

Abstract

This paper investigates the bounds on channel capacity and constellation shaping under memoryless mixed noise, which is composed of impulsive noise (IN) and white Gaussian noise (WGN). The capacity bounds are derived using the entropy power inequality and the dual expression of capacity. It is then shown that the proposed lower and upper bounds asymptotically converge to the true channel capacity, and the analytic asymptotic capacity expression is obtained. Leveraging this property, we design a low-complexity constellation shaping method that operates without iterative procedures. Simulation results demonstrate that the derived bounds are remarkably tight, and the shaped constellation achieves the highest mutual information among all considered baseline schemes.
Paper Structure (13 sections, 2 theorems, 23 equations, 2 figures)

This paper contains 13 sections, 2 theorems, 23 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Channel Noise Model
  4. Problem formulation
  5. Capacity Bounds
  6. Lower bound
  7. Upper bound
  8. Asymptotic analysis
  9. Low-complexity constellation shaping
  10. Geometric shaping
  11. Probabilistic shaping
  12. simulations
  13. conclusions

Key Result

Lemma 1

Assume the input $X$ satisfies the power constraint constraint_1, and the amplitude of the channel noise follows mixed_noise_model. Then, $\mathbb{E}_{Y}[|Y|^p]^{\frac{1}{p}}\leq P_0^{\frac{1}{p}}+\mathbb{E}_{N}[|N|^p]^{\frac{1}{p}}<+\infty$ for arbitrary $p<\alpha$.

Figures (2)

  • Figure 1: Comparison of channel capacity and bounds under various $\alpha$ and $\rho$.
  • Figure 2: Mutual information comparison between the low-complexity constellation shaping and baselines under different modulation orders with $(\alpha,\rho)=(1.5,0.5)$.

Theorems & Definitions (2)

  • Lemma 1
  • Theorem 1