Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2101.03650

The Degraded Discrete-Time Poisson Wiretap Channel

Morteza Soltani, Zouheir Rezki

Published Jan 11, 2021• 3 citations
arXivHTMLPDF

Abstract

This paper addresses the degraded discrete-time Poisson wiretap channel (DT--PWC) in an optical wireless communication system based on intensity modulation and direct detection. Subject to nonnegativity, peak- and average-intensity as well as bandwidth constraints, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points; one of them located at the origin. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with finitely many mass points. In general, the number of mass points of the optimal distributions is greater than two. This is in contrast with the degraded continuous-time PWC when the signaling bandwidth is not restricted and where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions. Furthermore, we extend our analysis to the case where only an average-intensity constraint is active. For this case, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with countably \textit{infinite} number of mass points, but with finitely many mass points in any bounded interval.

DOI
10.48550/arxiv.2101.03650

Related papers

Discrete-Time Poisson Optical Wiretap Channel with Peak Intensity Constraint

Morteza Soltani, Zouheir Rezki

This paper addresses the discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communications system based on intensity modulation and direct detection. Subject to nonnegativity and peak intensity as well as bandwidth constraints imposed on the channel input, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with a finite support. In general, the number of mass point of the optimal distributions are greater than two. This is in contrast with the continuous-time PWC where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions when the signaling bandwidth is not restricted. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the low intensity regime and observe that the secrecy capacity scales quadratically with the peak intensity constraint. Finally, Our numerical results indicate that there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2019•4 citations

The Rate-Equivocation Region of the Degraded Discrete-Time Poisson Wiretap Channel

Morteza Soltani, Zouheir Rezki

This paper addresses the degraded discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communication system based on intensity modulation and direct detection (IM-DD). Subject to nonnegativity, average-intensity, and bandwidth constraints, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with a countably infinite number of mass points, but with finitely many mass points in any bounded interval. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the regimes where the average intensity constraint either tends to zero (low-intensity) or tends to infinity (high-intensity). In the low-intensity regime, we observe that: when the channel gains of the legitimate receiver and the eavesdropper are identical, the secrecy capacity scales linearly in the average-intensity ε; whereas when the channel gains are different, the secrecy capacity scales, to within a constant, like$(\alpha_{B}-\alpha_{E})\mathcal{E}\log\log\frac{1}{\mathcal{E}}$, where αBand αEare the legitimate receiver's and the eavesdropper's channel gains, respectively. In the high-intensity regime, we establish that the secrecy capacity does not scale with the average intensity constraint.

IEEE International Symposium on Information Theory (ISIT)•Jul 12, 2021•1 citation

New Results on The Rate-Equivocation Region of The Optical Wiretap Channel with Input-Dependent Gaussian Noise with an Average-Intensity Constraint

Morteza Soltani, Zouheir Rezki

This paper studies the degraded optical wiretap channel with an input-dependent Gaussian noise when the channel input is only constrained by nonnegativity and average-intensity constraints. We consider the rate-equivocation region of this wiretap channel and through solving a convex optimization problem, we establish that discrete input distributions with an infinite number of mass points exhaust the entire rate-equivocation region of the degraded OWC-IDGN with non-negativity and average-intensity constraints. This result implies that when nonnegativity and average-intensity constraints are imposed on the channel input: 1) the secrecy-capacity-achieving input distribution of the degraded OWC-IDGN is discrete with an unbounded support, i.e., the support set of the optimal distribution is countably infinite; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a discrete distribution with an unbounded support set.

Information Theory and Applications Workshop (ITA)•Feb 2, 2020•2 citations

Optical Wiretap Channel With Input-Dependent Gaussian Noise Under Peak- and Average-Intensity Constraints

Morteza Soltani, Zouheir Rezki

This paper studies the optical wiretap channel with input-dependent Gaussian noise, in which the main distortion is caused by an additive Gaussian noise whose variance depends on the current signal strength. Subject to nonnegativity and peak-intensity constraints on the channel input, we first present a practical optical wireless communication scenario for which the considered wiretap channel is stochastically degraded. We then study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. Moreover, we show that the entire rate-equivocation region of this wiretap channel is also obtained by discrete input distributions with a finite support. Similar to the case of the Gaussian wiretap channel under a peak-power constraint, here too, we observe that under nonnegativity and peak-intensity constraints, there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously. Furthermore, we prove the optimality of discrete input distributions in the presence of an additional average intensity constraint. Finally, we shed light on the asymptotic behavior of the secrecy capacity in the low- and high-intensity regimes. In the low-intensity regime, the secrecy capacity scales quadratically with the peak-intensity constraint. On the other hand, in the high-intensity regime, the secrecy capacity does not scale with the constraint.

IEEE Transactions on Information Theory•Jun 28, 2018•23 citations

Results on the Rate-Equivocation Region of the Degraded Signal-Dependent Noise Wiretap Channel

Morteza Soltani, Zouheir Rezki

This letter studies the rate-equivocation region of a degraded signal-dependent noise wiretap channel (SDGN-WC), where the noise is Gaussian. This signal-dependent noise occurs in optical wireless communication (OWC) settings based on intensity modulation and direct detection (IM-DD). In this setup, the transmitted signals are nonnegative and are restricted by an average optical power constraint. We consider the rate-equivocation region of the degraded SDGN-WC and through solving a convex optimization problem, we establish that the support set of the optimal distributions must be countably infinite. Our result implies that when the transmitted optical signals are restricted by an average optical power: 1) the secrecy capacity is achieved by a distribution which has a countably infinite support set; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a distribution having a countably infinite support set.

IEEE Communications Letters•Jun 1, 2020•3 citations

The Degraded Poisson Wiretap Channel

Amine Laourine, Aaron B. Wagner

Providing security guarantees for wireless communication is critically important for today's applications. While previous work in this area has concentrated on radio frequency (RF) channels, providing security guarantees for RF channels is inherently difficult because they are prone to rapid variations due small scale fading. Wireless optical communication, on the other hand, is inherently more secure than RF communication due to the intrinsic aspects of the signal propagation in the optical and near-optical frequency range. In this paper, secure communication over wireless optical links is examined by studying the secrecy capacity of a direct detection system. For the degraded Poisson wiretap channel, a closed-form expression of the secrecy capacity is given. A complete characterization of the general rate-equivocation region is also presented. For achievability, an optimal code is explicitly constructed by using the structured code designed by Wyner for the Poisson channel. The converse is proved in two different ways: the first method relies only on simple properties of the conditional expectation and basic information theoretical inequalities, whereas the second method hinges on the recent link established between minimum mean square estimation and mutual information in Poisson channels.

arXiv:1004.0269•Apr 2, 2010•0 citations
This paper addresses the degraded discrete-time Poisson wiretap channel (DT--PWC) in an optical wireless communication system based on intensity modulation and direct detection. Subject to nonnegativity, peak- and average-intensity as well as bandwidth constraints, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points; one of them located at the origin. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with finitely many mass points. In general, the number of mass points of the optimal distributions is greater than two. This is in contrast with the degraded continuous-time PWC when the signaling bandwidth is not restricted and where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions. Furthermore, we extend our analysis to the case where only an average-intensity constraint is active. For this case, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with countably \textit{infinite} number of mass points, but with finitely many mass points in any bounded interval.
This paper addresses the discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communications system based on intensity modulation and direct detection. Subject to nonnegativity and peak intensity as well as bandwidth constraints imposed on the channel input, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with a finite support. In general, the number of mass point of the optimal distributions are greater than two. This is in contrast with the continuous-time PWC where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions when the signaling bandwidth is not restricted. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the low intensity regime and observe that the secrecy capacity scales quadratically with the peak intensity constraint. Finally, Our numerical results indicate that there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously.
This paper addresses the degraded discrete-time Poisson wiretap channel (DT-PWC) in an optical wireless communication system based on intensity modulation and direct detection (IM-DD). Subject to nonnegativity, average-intensity, and bandwidth constraints, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with a countably infinite number of mass points, but with finitely many mass points in any bounded interval. Additionally, we shed light on the asymptotic behavior of the secrecy capacity in the regimes where the average intensity constraint either tends to zero (low-intensity) or tends to infinity (high-intensity). In the low-intensity regime, we observe that: when the channel gains of the legitimate receiver and the eavesdropper are identical, the secrecy capacity scales linearly in the average-intensity ε; whereas when the channel gains are different, the secrecy capacity scales, to within a constant, like(αB−αE)Elog⁡log⁡1E(\alpha_{B}-\alpha_{E})\mathcal{E}\log\log\frac{1}{\mathcal{E}}(αB​−αE​)EloglogE1​, where αBand αEare the legitimate receiver's and the eavesdropper's channel gains, respectively. In the high-intensity regime, we establish that the secrecy capacity does not scale with the average intensity constraint.
This paper studies the degraded optical wiretap channel with an input-dependent Gaussian noise when the channel input is only constrained by nonnegativity and average-intensity constraints. We consider the rate-equivocation region of this wiretap channel and through solving a convex optimization problem, we establish that discrete input distributions with an infinite number of mass points exhaust the entire rate-equivocation region of the degraded OWC-IDGN with non-negativity and average-intensity constraints. This result implies that when nonnegativity and average-intensity constraints are imposed on the channel input: 1) the secrecy-capacity-achieving input distribution of the degraded OWC-IDGN is discrete with an unbounded support, i.e., the support set of the optimal distribution is countably infinite; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a discrete distribution with an unbounded support set.
This paper studies the optical wiretap channel with input-dependent Gaussian noise, in which the main distortion is caused by an additive Gaussian noise whose variance depends on the current signal strength. Subject to nonnegativity and peak-intensity constraints on the channel input, we first present a practical optical wireless communication scenario for which the considered wiretap channel is stochastically degraded. We then study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. Moreover, we show that the entire rate-equivocation region of this wiretap channel is also obtained by discrete input distributions with a finite support. Similar to the case of the Gaussian wiretap channel under a peak-power constraint, here too, we observe that under nonnegativity and peak-intensity constraints, there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously. Furthermore, we prove the optimality of discrete input distributions in the presence of an additional average intensity constraint. Finally, we shed light on the asymptotic behavior of the secrecy capacity in the low- and high-intensity regimes. In the low-intensity regime, the secrecy capacity scales quadratically with the peak-intensity constraint. On the other hand, in the high-intensity regime, the secrecy capacity does not scale with the constraint.
This letter studies the rate-equivocation region of a degraded signal-dependent noise wiretap channel (SDGN-WC), where the noise is Gaussian. This signal-dependent noise occurs in optical wireless communication (OWC) settings based on intensity modulation and direct detection (IM-DD). In this setup, the transmitted signals are nonnegative and are restricted by an average optical power constraint. We consider the rate-equivocation region of the degraded SDGN-WC and through solving a convex optimization problem, we establish that the support set of the optimal distributions must be countably infinite. Our result implies that when the transmitted optical signals are restricted by an average optical power: 1) the secrecy capacity is achieved by a distribution which has a countably infinite support set; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a distribution having a countably infinite support set.
Providing security guarantees for wireless communication is critically important for today's applications. While previous work in this area has concentrated on radio frequency (RF) channels, providing security guarantees for RF channels is inherently difficult because they are prone to rapid variations due small scale fading. Wireless optical communication, on the other hand, is inherently more secure than RF communication due to the intrinsic aspects of the signal propagation in the optical and near-optical frequency range. In this paper, secure communication over wireless optical links is examined by studying the secrecy capacity of a direct detection system. For the degraded Poisson wiretap channel, a closed-form expression of the secrecy capacity is given. A complete characterization of the general rate-equivocation region is also presented. For achievability, an optimal code is explicitly constructed by using the structured code designed by Wyner for the Poisson channel. The converse is proved in two different ways: the first method relies only on simple properties of the conditional expectation and basic information theoretical inequalities, whereas the second method hinges on the recent link established between minimum mean square estimation and mutual information in Poisson channels.