A Risk-Aware Framework for Covert Quantum Communication under Stochastic Channel Uncertainty

Abbas Arghavani; Alessandro Papadopoulos; Maryam Amiri; Shahid Raza

arxiv: 2605.18928 · v1 · pith:BL5S25XMnew · submitted 2026-05-18 · 🪐 quant-ph · cs.CR· eess.SP

A Risk-Aware Framework for Covert Quantum Communication under Stochastic Channel Uncertainty

Abbas Arghavani , Shahid Raza , Maryam Amiri , Alessandro Papadopoulos This is my paper

Pith reviewed 2026-05-20 11:19 UTC · model grok-4.3

classification 🪐 quant-ph cs.CReess.SP

keywords covert quantum communicationstochastic optimizationchance constraintsfree-space optical linksrisk-aware frameworklog-normal fadingcovert throughput

0 comments

The pith

Modeling transmissivity and noise as random variables with chance constraints lets a risk-aware framework expand feasible regions for covert quantum communication and boost throughput by more than an order of magnitude.

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

The paper introduces a stochastic optimization framework that treats channel transmissivity and background noise as random variables rather than fixed values. It converts the requirements for hiding the communication and for reliable decoding into chance constraints that allow a small, budgeted probability of outage. Quantile reformulations turn these probabilistic requirements into deterministic constraints that can be optimized for throughput while respecting explicit risk levels. Monte Carlo trials under log-normal fading and thermal noise confirm that the resulting designs open up larger operating regions and deliver substantially higher covert rates than deterministic approaches.

Core claim

Expressing covertness and reliability guarantees through chance constraints with explicit outage budgets ε_cov and ε_rel recasts covert quantum communication design as a risk-calibrated resource-allocation problem; quantile-based reformulations of the outage constraints then characterize feasible operating regions under stochastic uncertainty in transmissivity and background noise, showing that modest relaxations in acceptable covertness-outage risk can yield large throughput gains.

What carries the argument

Chance constraints with outage budgets ε_cov and ε_rel, reformulated using quantiles of the random transmissivity and noise distributions to produce a risk-calibrated optimization problem.

If this is right

Modest relaxations in acceptable covertness-outage risk produce large throughput gains.
Aggressive optimization breaks covertness guarantees outside sparse-transmission regimes.
The framework expands feasible operating regions under log-normal fading and stochastic thermal noise.
Degradation boundaries are identified beyond which covert operation becomes unreliable.

Where Pith is reading between the lines

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

Similar chance-constraint methods could be applied to quantum key distribution to improve secret-key rates in turbulent free-space channels.
Real-time channel statistics could be used to adapt the outage budgets dynamically during a session.
Experimental comparisons against worst-case designs in satellite or ground-to-ground links would quantify the practical throughput improvement.
Network-level extensions that allocate risk budgets across multiple links could reveal end-to-end trade-offs for large-scale covert networks.

Load-bearing premise

The statistical distributions of transmissivity and background noise are known or accurately estimated in advance and the chosen outage budgets correctly represent the acceptable risk levels for the application.

What would settle it

Monte Carlo trials or field measurements in which the realized frequency of covertness violations exceeds the budgeted ε_cov when the framework is applied under the assumed log-normal and thermal-noise models.

Figures

Figures reproduced from arXiv: 2605.18928 by Abbas Arghavani, Alessandro Papadopoulos, Maryam Amiri, Shahid Raza.

**Figure 2.** Figure 2: The CQC channel model, where Alice transmits a signal [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: illustrates the bilinear geometry of the throughput objective . However, the main simplification in the riskconstrained formulation does not come merely from observing nonconvexity; it comes from the CQC-specific reduction of stochastic physical-layer uncertainty to calibrated outage variables, which converts the chance constraints into [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

**Figure 4.** Figure 4: Scaling of total scheduled covert qubits ( [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗

**Figure 5.** Figure 5: Impact of the nominal channel-quality scenario on th [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗

**Figure 6.** Figure 6: Effect of transmi ance volatility on the symmetric-r [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: Surface of total scheduled covert qubits ( [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗

**Figure 8.** Figure 8: Sensitivity along the symmetric-budget line [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗

**Figure 9.** Figure 9: Exploratory sweeps in the risk-adjusted model. The p [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗

**Figure 10.** Figure 10: Exploratory heatmaps of the numerically selected o [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗

read the original abstract

Covert quantum communication (CQC) seeks to hide not only message content but also the existence of communication. Existing CQC models usually assume deterministic or worst-case channel conditions, which are difficult to justify in realistic free-space optical and quantum links affected by turbulence, fluctuating background radiance, and stochastic detector noise. We propose a stochastic risk-aware optimization framework for CQC under uncertain physical-layer conditions. By modeling transmissivity and background noise as random variables, we express covertness and reliability guarantees through chance constraints with explicit outage budgets $\epsilon_{\text{cov}}$ and $\epsilon_{\text{rel}}$. This recasts CQC design as a risk-calibrated resource-allocation problem balancing throughput, covertness, reliability, and communication privacy. We derive quantile-based reformulations of the outage constraints, characterize feasible operating regions under stochastic uncertainty, and introduce a complementary risk-adjusted utility formulation to expose throughput-risk trade-offs. The analysis reveals that modest relaxations in acceptable covertness-outage risk can yield large throughput gains, while aggressive optimization may break covertness outside sparse-transmission regimes. Monte Carlo results under log-normal fading and stochastic thermal noise show that the framework expands feasible operating regions, improves covert throughput by more than an order of magnitude, and identifies degradation boundaries beyond which covert operation becomes unreliable. These results move CQC closer to realistic secure quantum networking for free-space, satellite, and low-probability-of-detection applications.

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.

Desk Editor's Note private letter to a colleague

The paper adds chance constraints to handle random channel effects in covert quantum communication, but the performance claims only hold if the distributions are known exactly.

read the letter

The main thing to know is that this work recasts covert quantum communication as a risk-calibrated optimization problem with explicit outage budgets for covertness and reliability under random transmissivity and noise. That moves past the usual deterministic or worst-case assumptions and uses quantile reformulations plus a risk-adjusted utility to expose throughput-risk trade-offs. Monte Carlo runs under log-normal fading and stochastic thermal noise are used to show expanded feasible regions and throughput gains when the risk budgets are relaxed modestly. This is genuinely new relative to the models cited in the abstract, and the framework does a clean job of balancing the competing goals while flagging where aggressive settings break covertness outside sparse regimes. The low circularity burden and use of external stochastic models plus sampling are also positives. The soft spot is exactly what the stress-test flags: the guarantees and the reported order-of-magnitude improvements require that the channel distributions (including all parameters) are known perfectly in advance. Real free-space turbulence often needs estimation from limited samples, and the paper provides no sensitivity analysis or robust counterpart for mismatch. If those assumptions slip, the realized outage rates can exceed the budgeted epsilons and erode both covertness and reliability. The abstract-level description leaves the exact derivations and verification steps opaque, so the strength of the constraint conversions is hard to judge without the full text. This is for researchers focused on practical free-space or satellite quantum links who already work with stochastic optimization. A reader looking for concrete ways to incorporate uncertainty into covert designs will find usable ideas, though they should treat the numerical gains as provisional. It deserves peer review because the core formulation tackles a real practical gap and is grounded enough to benefit from referee feedback on the robustness side.

Referee Report

3 major / 2 minor

Summary. The paper proposes a stochastic risk-aware optimization framework for covert quantum communication (CQC) under uncertain physical-layer conditions such as turbulence and fluctuating noise. It models transmissivity and background noise as random variables, recasts covertness and reliability as chance constraints with explicit outage budgets ε_cov and ε_rel, derives quantile-based reformulations for tractable resource allocation, introduces a risk-adjusted utility to expose throughput-risk trade-offs, and uses Monte Carlo simulations under log-normal fading and stochastic thermal noise to claim expanded feasible operating regions, order-of-magnitude covert throughput gains, and identification of degradation boundaries.

Significance. If the results hold, the framework is significant for moving CQC toward realistic free-space, satellite, and low-probability-of-detection applications by replacing deterministic or worst-case assumptions with probabilistic risk calibration. The Monte Carlo validation under explicit stochastic models and the focus on outage budgets provide concrete, falsifiable performance insights that could inform practical system design.

major comments (3)

[Abstract] Abstract: The claim that quantile-based reformulations yield tractable problems while preserving chance-constraint guarantees is presented without explicit derivation steps, equivalence proofs, or approximation error bounds, which is load-bearing for the central tractability and correctness assertions.
[Monte Carlo results] Monte Carlo results section: The reported order-of-magnitude throughput improvements and expanded feasible regions are shown only under perfectly known log-normal parameters and noise distributions; no sensitivity analysis to parameter estimation errors or distribution mismatch is included, directly undermining the practical validity of the ε_cov and ε_rel guarantees.
[Risk-adjusted utility formulation] Risk-adjusted utility formulation: The characterization of throughput-risk trade-offs is introduced but lacks sufficient detail on the optimization procedure, numerical solver, or how the utility is computed from the quantile reformulations, making reproducibility and assessment of the trade-off claims difficult.

minor comments (2)

Consider adding a summary table listing all random variables, their assumed distributions, and the specific parameter values used in the Monte Carlo experiments for improved clarity and reproducibility.
[Abstract] The abstract references 'communication privacy' as part of the balancing act, but this element is not elaborated in the framework description; clarify its mathematical role or remove if not central.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the presentation and practical relevance of the results.

read point-by-point responses

Referee: [Abstract] Abstract: The claim that quantile-based reformulations yield tractable problems while preserving chance-constraint guarantees is presented without explicit derivation steps, equivalence proofs, or approximation error bounds, which is load-bearing for the central tractability and correctness assertions.

Authors: The abstract serves as a high-level overview. The quantile reformulations are derived in Section III, where we show that the chance constraints on covertness and reliability are equivalently recast as deterministic quantile constraints for continuous random variables, with no approximation error in the reformulation itself. Equivalence follows directly from the definition of the quantile function. We will revise the abstract to briefly reference this equivalence and point to Section III for the full derivation and proofs. revision: partial
Referee: [Monte Carlo results] Monte Carlo results section: The reported order-of-magnitude throughput improvements and expanded feasible regions are shown only under perfectly known log-normal parameters and noise distributions; no sensitivity analysis to parameter estimation errors or distribution mismatch is included, directly undermining the practical validity of the ε_cov and ε_rel guarantees.

Authors: We agree that the current results assume known distribution parameters, which is a common starting point to isolate the benefits of the risk-aware formulation. This leaves open questions about robustness to estimation errors. In the revision we will add a dedicated sensitivity analysis subsection that perturbs the log-normal parameters and considers mismatched distributions, quantifying the resulting impact on the realized outage probabilities relative to the target ε_cov and ε_rel. revision: yes
Referee: [Risk-adjusted utility formulation] Risk-adjusted utility formulation: The characterization of throughput-risk trade-offs is introduced but lacks sufficient detail on the optimization procedure, numerical solver, or how the utility is computed from the quantile reformulations, making reproducibility and assessment of the trade-off claims difficult.

Authors: The risk-adjusted utility is defined in Section IV as a convex program that directly substitutes the quantile expressions into the objective and constraints. It is solved with CVXPY using the MOSEK interior-point solver. To improve reproducibility we will add pseudocode outlining the end-to-end procedure, explicit solver tolerances, and a step-by-step description of how the quantile values are obtained from the Monte Carlo samples before being inserted into the utility optimization. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivations rely on external stochastic models and independent Monte Carlo validation

full rationale

The paper models transmissivity and background noise as random variables drawn from standard external distributions (log-normal fading and stochastic thermal noise), formulates chance constraints using explicit outage budgets ε_cov and ε_rel, derives quantile-based reformulations via standard mathematical techniques for tractable optimization, characterizes feasible regions and risk-adjusted utilities, and validates performance claims through Monte Carlo sampling. No claimed result or prediction reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain; the central framework remains independent of its own outputs and uses externally falsifiable models and simulation methods.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on domain assumptions about channel statistics and standard optimization theory; no new physical entities are postulated and no free parameters are fitted to data within the reported results.

axioms (2)

domain assumption Transmissivity and background noise can be modeled as independent random variables with known distributions (log-normal fading and stochastic thermal noise).
Invoked when expressing covertness and reliability through chance constraints; stated in the abstract description of the modeling step.
domain assumption Chance constraints with user-specified outage budgets ε_cov and ε_rel provide meaningful probabilistic guarantees for covertness and reliability.
Core modeling choice that converts the stochastic problem into a risk-calibrated optimization; appears when the framework is introduced.

pith-pipeline@v0.9.0 · 5795 in / 1477 out tokens · 31456 ms · 2026-05-20T11:19:05.246785+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We derive quantile-based reformulations of the outage constraints... Monte Carlo results under log-normal fading
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

risk-constrained optimization that maximizes covert throughput under explicit probabilistic budgets

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · 2 internal anchors

[1]

Alexander

Stephen B. Alexander. 1997. Optical Communication Receiver Design . SPIE Press, Bellingham, W A

work page 1997
[2]

Evan JD Anderson, Michael S Bullock, Filip Rozpędek, and Boulat A Bash. 2025. Achievability of covert quantum commun ication. In 2025 IEEE International Symposium on Information Theory (ISIT) . IEEE, 1–6

work page 2025
[3]

Evan JD Anderson, Christopher K Eyre, Isabel M Dailey, Fi lip Rozpędek, and Boulat A Bash. 2024. Square Root Law for Cov ert Quantum Commu- nication over Optical Channels. In IEEE Int. Conf. Quantum Computing and Engineering (QCE) . 1817–1823

work page 2024
[4]

Evan J. D. Anderson, Christopher K. Eyre, Isabel M. Daile y, Filip Rozpędek, and Boulat A. Bash. 2024. Covert Quantum C ommunication Over Optical Channels. arXiv:2401.06764 [quant-ph] Preprint

work page arXiv 2024
[5]

Andrews and Melissa K

Larry C. Andrews and Melissa K. Beason. 2023. Laser Beam Propagation in Random Media: New and Advanced Topi cs. SPIE Press, Bellingham, W A. doi:10.1117/3.2643989

work page doi:10.1117/3.2643989 2023
[6]

Abbas Arghavani. 2026. Conﬂict-Aware Robust Design for Covert Wireless Communications. arXiv preprint arXiv:2604.13122 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026
[7]

Abbas Arghavani, Anders Ahlén, André Teixeira, and Subh rakanti Dey. 2021. A game-theoretic approach to covert communications in the presence of multiple colluding wardens. In IEEE Wireless Communications and Networking Conference (W CNC). 1–7

work page 2021
[8]

Abbas Arghavani, Subhrakanti Dey, and Anders Ahlén. 202 3. Covert outage minimization in the presence of multiple wa rdens. IEEE Trans. Signal Processing 71 (2023), 686–700

work page 2023
[9]

Abbas Arghavani, Alessandro V Papadopoulos, Vahid Azim i Mousolou, Giuseppe Nebbione, and Shahid Raza. 2026. Robus t Covert Quantum Communication under Bounded Channel Uncertainty. arXiv preprint arXiv:2604.13116 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026
[10]

Bash, Dennis Goeckel, and Don Towsley

Boulat A. Bash, Dennis Goeckel, and Don Towsley. 2013. L imits of reliable communication with low probability of det ection on A WGN channels. IEEE J. Selected Areas in Communication 31, 9 (2013), 1921–1930

work page 2013
[11]

Helstrom

Carl W. Helstrom. 1976. Quantum Detection and Estimation Theory . Academic Press, New York

work page 1976
[12]

Mohammad Ali Khalighi and Murat Uysal. 2014. Survey on f ree space optical communication: A communication theory pe rspective. IEEE commu- nications surveys & tutorials 16, 4 (2014), 2231–2258. Manuscript submitted to ACM 28 Arghavani et al

work page 2014
[13]

Madhushanka Padmal, Johan Engstrand, Abbas Arghavani , Subhrakanti Dey, Robin Augustine, Riku Jäntti, and Thiemo Voigt. 2025. Fat Tissue- Based In-Body Covert Communication. In 2025 IEEE 26th International Symposium on a World of Wireles s, Mobile and Multimedia Networks (WoW- MoM). 61–71

work page 2025
[14]

Tamara V Sobers, Boulat A Bash, Saikat Guha, Don Towsley , and Dennis Goeckel. 2017. Covert communication in the pres ence of an uninformed jammer. IEEE Trans. on Wireless Communications 16, 9 (2017), 6193–6206

work page 2017
[15]

Ramin Soltani, Dennis Goeckel, Don Towsley, Boulat A Bash, and Saikat Guha. 2018. Covert wireless communication with artiﬁcial noise generation. IEEE Trans. on Wireless Communications 17, 11 (2018), 7252–7267

work page 2018
[16]

Mehrdad Tahmasbi, Boulat A Bash, Saikat Guha, and Matth ieu Bloch. 2021. Signaling for covert quantum sensing. In IEEE International Symposium on Information Theory (ISIT) . 1041–1045

work page 2021
[17]

Wornell, and Lizhong Zheng

Ligong Wang, Gregory W. Wornell, and Lizhong Zheng. 201 6. Fundamental limits of communication with low probabilit y of detection. IEEE Trans. Information Theory 62, 6 (2016), 3493–3503

work page 2016
[18]

Mark M. Wilde. 2017. Quantum Information Theory (2nd ed.). Cambridge University Press, Cambridge. A Proof of Theorem 1 (Optimal risk-constrained throughput) Consider the risk-constrained program (10)–(12) with obje ctive /u1D447(/u1D45E, /u1D445)= /u1D45E/u1D445, probabilistic constraints P [ /u1D45E> 2/u1D6FF √ /u1D45B/u1D450cov (/u1D702,/u1D45B/u1D435) ...

work page 2017

[1] [1]

Alexander

Stephen B. Alexander. 1997. Optical Communication Receiver Design . SPIE Press, Bellingham, W A

work page 1997

[2] [2]

Evan JD Anderson, Michael S Bullock, Filip Rozpędek, and Boulat A Bash. 2025. Achievability of covert quantum commun ication. In 2025 IEEE International Symposium on Information Theory (ISIT) . IEEE, 1–6

work page 2025

[3] [3]

Evan JD Anderson, Christopher K Eyre, Isabel M Dailey, Fi lip Rozpędek, and Boulat A Bash. 2024. Square Root Law for Cov ert Quantum Commu- nication over Optical Channels. In IEEE Int. Conf. Quantum Computing and Engineering (QCE) . 1817–1823

work page 2024

[4] [4]

Evan J. D. Anderson, Christopher K. Eyre, Isabel M. Daile y, Filip Rozpędek, and Boulat A. Bash. 2024. Covert Quantum C ommunication Over Optical Channels. arXiv:2401.06764 [quant-ph] Preprint

work page arXiv 2024

[5] [5]

Andrews and Melissa K

Larry C. Andrews and Melissa K. Beason. 2023. Laser Beam Propagation in Random Media: New and Advanced Topi cs. SPIE Press, Bellingham, W A. doi:10.1117/3.2643989

work page doi:10.1117/3.2643989 2023

[6] [6]

Abbas Arghavani. 2026. Conﬂict-Aware Robust Design for Covert Wireless Communications. arXiv preprint arXiv:2604.13122 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026

[7] [7]

Abbas Arghavani, Anders Ahlén, André Teixeira, and Subh rakanti Dey. 2021. A game-theoretic approach to covert communications in the presence of multiple colluding wardens. In IEEE Wireless Communications and Networking Conference (W CNC). 1–7

work page 2021

[8] [8]

Abbas Arghavani, Subhrakanti Dey, and Anders Ahlén. 202 3. Covert outage minimization in the presence of multiple wa rdens. IEEE Trans. Signal Processing 71 (2023), 686–700

work page 2023

[9] [9]

Abbas Arghavani, Alessandro V Papadopoulos, Vahid Azim i Mousolou, Giuseppe Nebbione, and Shahid Raza. 2026. Robus t Covert Quantum Communication under Bounded Channel Uncertainty. arXiv preprint arXiv:2604.13116 (2026)

work page internal anchor Pith review Pith/arXiv arXiv 2026

[10] [10]

Bash, Dennis Goeckel, and Don Towsley

Boulat A. Bash, Dennis Goeckel, and Don Towsley. 2013. L imits of reliable communication with low probability of det ection on A WGN channels. IEEE J. Selected Areas in Communication 31, 9 (2013), 1921–1930

work page 2013

[11] [11]

Helstrom

Carl W. Helstrom. 1976. Quantum Detection and Estimation Theory . Academic Press, New York

work page 1976

[12] [12]

Mohammad Ali Khalighi and Murat Uysal. 2014. Survey on f ree space optical communication: A communication theory pe rspective. IEEE commu- nications surveys & tutorials 16, 4 (2014), 2231–2258. Manuscript submitted to ACM 28 Arghavani et al

work page 2014

[13] [13]

Madhushanka Padmal, Johan Engstrand, Abbas Arghavani , Subhrakanti Dey, Robin Augustine, Riku Jäntti, and Thiemo Voigt. 2025. Fat Tissue- Based In-Body Covert Communication. In 2025 IEEE 26th International Symposium on a World of Wireles s, Mobile and Multimedia Networks (WoW- MoM). 61–71

work page 2025

[14] [14]

Tamara V Sobers, Boulat A Bash, Saikat Guha, Don Towsley , and Dennis Goeckel. 2017. Covert communication in the pres ence of an uninformed jammer. IEEE Trans. on Wireless Communications 16, 9 (2017), 6193–6206

work page 2017

[15] [15]

Ramin Soltani, Dennis Goeckel, Don Towsley, Boulat A Bash, and Saikat Guha. 2018. Covert wireless communication with artiﬁcial noise generation. IEEE Trans. on Wireless Communications 17, 11 (2018), 7252–7267

work page 2018

[16] [16]

Mehrdad Tahmasbi, Boulat A Bash, Saikat Guha, and Matth ieu Bloch. 2021. Signaling for covert quantum sensing. In IEEE International Symposium on Information Theory (ISIT) . 1041–1045

work page 2021

[17] [17]

Wornell, and Lizhong Zheng

Ligong Wang, Gregory W. Wornell, and Lizhong Zheng. 201 6. Fundamental limits of communication with low probabilit y of detection. IEEE Trans. Information Theory 62, 6 (2016), 3493–3503

work page 2016

[18] [18]

Mark M. Wilde. 2017. Quantum Information Theory (2nd ed.). Cambridge University Press, Cambridge. A Proof of Theorem 1 (Optimal risk-constrained throughput) Consider the risk-constrained program (10)–(12) with obje ctive /u1D447(/u1D45E, /u1D445)= /u1D45E/u1D445, probabilistic constraints P [ /u1D45E> 2/u1D6FF √ /u1D45B/u1D450cov (/u1D702,/u1D45B/u1D435) ...

work page 2017