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arxiv: 2503.09825 · v2 · submitted 2025-03-12 · 💻 cs.IT · math.IT

Information-Energy Capacity Region for SLIPT Systems over Lognormal Fading Channels: A Theoretical and Learning-Based Analysis

Nizar Khalfet , Kapila W. S. Palitharathna , Symeon Chatzinotas , Ioannis Krikidis This is my paper

Pith reviewed 2026-05-23 00:05 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords SLIPTlognormal fadinginformation-energy capacity regiondiscrete input distributionrate-power trade-offgenerative adversarial networks
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The pith

SLIPT systems over lognormal fading achieve their information-energy capacity region with a discrete input distribution of finite mass points.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies Smith's framework to the information-energy capacity region of simultaneous lightwave information and power transfer systems in lognormal fading, which models optical wireless channels such as underwater and atmospheric links. It establishes that the optimal input distribution is discrete and supported on only a finite number of mass points. The analysis examines the locations and properties of these points at regime transitions to clarify the inherent rate-power trade-off. A generative adversarial network framework is introduced to numerically estimate and optimize the capacity region under practical constraints. Numerical evaluations confirm that fading strength materially changes the achievable region.

Core claim

By applying Smith's framework, the optimal input distribution for the information-energy capacity region of SLIPT systems over lognormal fading channels is discrete, characterized by a finite number of mass points. The properties of these mass points, especially at the transition points, reveal critical insights into the rate-power trade-off inherent in SLIPT systems.

What carries the argument

Smith's framework applied to the joint amplitude and power constrained SLIPT channel under lognormal fading, which proves that the capacity-achieving distribution must be discrete with finitely many points.

If this is right

  • The capacity region boundary is obtained by optimizing mutual information and harvested power over a finite discrete support.
  • Transitions between active mass points mark the operating points where the marginal trade-off between information rate and harvested energy changes.
  • Lognormal fading parameters shift both the number and locations of the mass points that achieve the boundary.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Capacity computation algorithms can iterate over candidate numbers of mass points until the boundary stabilizes, avoiding continuous optimization.
  • The same discreteness result may apply to other multiplicative fading distributions that preserve the convexity properties used in the proof.
  • The GAN estimator could be extended to include additional practical limits such as peak optical intensity or eye-safety constraints.

Load-bearing premise

Smith's framework for capacity analysis extends directly and without modification to the SLIPT setting over lognormal fading, including the amplitude and power constraints specific to simultaneous information and energy transfer.

What would settle it

A direct computation or exhaustive numerical search that produces an optimal input distribution requiring infinitely many mass points or a continuous density component would falsify the discreteness claim.

Figures

Figures reproduced from arXiv: 2503.09825 by Ioannis Krikidis, Kapila W. S. Palitharathna, Nizar Khalfet, Symeon Chatzinotas.

Figure 1
Figure 1. Figure 1: A SLIPT system over a lognormal-fading channel with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Proposed information-energy capacity learning frame [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Neural networks used in CIECL. (a) Generator. (b) Discriminator. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Optimal input distribution learned by CORTICAL at [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The optimal mass points versus PP constraint; [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Information-energy capacity region with different PP [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

This paper presents a comprehensive analysis of the information-energy capacity region for simultaneous lightwave information and power transfer (SLIPT) systems over lognormal fading channels. Unlike conventional studies that primarily focus on additive white Gaussian noise channels, we study the complex impact of lognormal fading, which is prevalent in optical wireless communication systems such as underwater and atmospheric channels. By applying the Smith's framework for these channels, we demonstrate that the optimal input distribution is discrete, characterized by a finite number of mass points. We further investigate the properties of these mass points, especially at the transition points, to reveal critical insights into the rate-power trade-off inherent in SLIPT systems. Additionally, we introduce a novel cooperative information-energy capacity learning framework, leveraging generative adversarial networks, to effectively estimate and optimize the information-energy capacity region under practical constraints. Numerical results validate our theoretical findings, illustrating the significant influence of channel fading on system performance. The insights and methodologies presented in this work provide a solid foundation for the design and optimization of future SLIPT systems operating in challenging environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper analyzes the information-energy capacity region for SLIPT systems over lognormal fading channels. It applies Smith's framework to establish that the optimal input distribution is discrete with a finite number of mass points, examines mass-point properties at transition points for rate-power trade-offs, and introduces a GAN-based cooperative learning framework to estimate the region under practical constraints. Numerical results are presented to validate the theoretical findings and illustrate fading effects.

Significance. If the applicability of Smith's framework is rigorously justified, the work would provide useful insights into the rate-power trade-off for SLIPT in lognormal fading environments common to optical wireless links. The GAN estimation method offers a practical tool for capacity region computation, and the numerical validation supplies concrete performance comparisons.

major comments (3)
  1. [§III] §III (theoretical analysis): The manuscript states that Smith's framework is applied directly to conclude discreteness of the optimal input distribution, but does not verify that the effective conditional density p(y|x) = E_H[p(y|x,H)] under multiplicative lognormal fading satisfies the analyticity and strict concavity conditions, nor that the joint amplitude-plus-energy-harvesting constraint set remains compact and convex in the required topology.
  2. [§III] §III, Eq. (capacity region definition): The objective is the information-energy region rather than scalar capacity; the paper does not show that the vector-valued objective and the intersection of amplitude and average-power constraints preserve the hypotheses needed for the finite-mass-point result.
  3. [§IV] §IV (mass-point properties): The analysis of mass-point locations and transition points is presented without an explicit derivation confirming that the averaged lognormal channel preserves the strict concavity or the supporting-hyperplane arguments used in the original Smith result.
minor comments (2)
  1. [§II] Notation for the energy-harvesting constraint and the fading-averaged mutual information should be introduced with explicit definitions before the capacity-region optimization is stated.
  2. [§V] Figure captions for the numerical results should include the specific parameter values (e.g., fading variance, SNR range) used in each plot.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which identify areas requiring additional rigor in the theoretical justification. We address each major comment point by point below and will incorporate the necessary verifications and derivations in the revised manuscript.

read point-by-point responses

  1. Referee: [§III] §III (theoretical analysis): The manuscript states that Smith's framework is applied directly to conclude discreteness of the optimal input distribution, but does not verify that the effective conditional density p(y|x) = E_H[p(y|x,H)] under multiplicative lognormal fading satisfies the analyticity and strict concavity conditions, nor that the joint amplitude-plus-energy-harvesting constraint set remains compact and convex in the required topology.

    Authors: We acknowledge that the current manuscript applies Smith's framework without an explicit verification of the conditions for the effective channel. In the revision, we will add a dedicated subsection in §III that proves the averaged conditional density p(y|x) satisfies analyticity and strict concavity, and that the joint constraint set is compact and convex in the appropriate topology. revision: yes

  2. Referee: [§III] §III, Eq. (capacity region definition): The objective is the information-energy region rather than scalar capacity; the paper does not show that the vector-valued objective and the intersection of amplitude and average-power constraints preserve the hypotheses needed for the finite-mass-point result.

    Authors: We agree that the vector-valued nature of the capacity region and the combined constraints require explicit justification. We will revise the capacity region definition in §III to demonstrate that the hypotheses of Smith's framework continue to hold for the vector objective and the intersection of amplitude and average-power constraints. revision: yes

  3. Referee: [§IV] §IV (mass-point properties): The analysis of mass-point locations and transition points is presented without an explicit derivation confirming that the averaged lognormal channel preserves the strict concavity or the supporting-hyperplane arguments used in the original Smith result.

    Authors: The mass-point analysis in §IV builds on the discreteness result from §III. In the revision we will insert an explicit derivation confirming that the averaged lognormal channel preserves strict concavity and the supporting-hyperplane arguments, thereby rigorously supporting the transition-point properties. revision: yes

Circularity Check

0 steps flagged

No circularity: external Smith's framework applied; GAN estimator introduced as new method

full rationale

The paper's central theoretical claim applies Smith's framework (an external result on discrete optimal inputs under amplitude constraints) to the SLIPT lognormal setting and states that discreteness follows. The learning component introduces a novel GAN-based cooperative framework to estimate the region under constraints. No self-citation load-bearing steps, self-definitional reductions, or fitted inputs renamed as predictions appear in the abstract or described derivation. The derivation chain remains self-contained against the cited external framework and the new estimator; no equations reduce to their own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Paper rests on applicability of Smith's framework to the new setting and on the validity of GAN training for capacity estimation; no new physical entities introduced.

axioms (1)
  • domain assumption Smith's framework applies directly to SLIPT over lognormal fading without additional SLIPT-specific modifications
    Invoked when stating optimal input is discrete with finite mass points.

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Reference graph

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