pith. sign in

arxiv: 1906.09512 · v1 · pith:JPXOJEHQnew · submitted 2019-06-22 · 💻 cs.IT · cs.PF· math.IT

On the Secrecy Rate of Spatial Modulation Based Indoor Visible Light Communications

Jin-Yuan Wang , Hong Ge , Min Lin , Jun-Bo Wang , Jianxin Dai , Mohamed-Slim Alouini This is my paper

Pith reviewed 2026-05-25 17:39 UTC · model grok-4.3

classification 💻 cs.IT cs.PFmath.IT
keywords spatial modulationvisible light communicationsecrecy ratephysical layer securitytransmitter selectionoptical intensity constraintsindoor VLC
0
0 comments X

The pith

The paper derives lower and upper bounds on secrecy rate for spatial modulation in indoor VLC systems under optical intensity constraints and identifies a greedy transmitter selection scheme as optimal.

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

The work focuses on physical-layer security in a spatial modulation visible light communication setup with multiple transmitters, one legitimate receiver, and a passive eavesdropper. Only one transmitter activates at a time, chosen either uniformly or via channel-aware methods. Lower and upper bounds on the achievable secrecy rate are obtained for two cases: one limited by non-negativity and average optical power, the other adding a peak optical power limit. Asymptotic analysis at high SNR shows the bounds remain close, and numerical comparisons indicate the greedy selection method yields the highest secrecy rate among the three schemes considered.

Core claim

For spatial modulation indoor VLC with a passive eavesdropper, lower and upper bounds on the secrecy rate are derived under non-negativity plus average optical intensity constraints and under the additional peak optical intensity constraint. The bounds are shown to be tight by numerical evaluation, with only small gaps remaining at high SNR. A greedy selection scheme for choosing the active transmitter is proposed and demonstrated to outperform both uniform selection and channel-adaptive selection.

What carries the argument

Spatial modulation with active-transmitter selection (uniform, channel-adaptive, or greedy) applied to the indoor VLC channel model under non-negativity and optical-intensity constraints.

If this is right

  • At high SNR the secrecy-rate bounds exhibit only small gaps, allowing the lower bound to serve as a reliable performance predictor.
  • The greedy selection scheme consistently achieves the highest secrecy rate of the three transmitter-selection methods examined.
  • The derived bounds apply separately to the average-power-only constraint set and to the joint average-plus-peak constraint set.
  • Asymptotic high-SNR expressions for the bounds can be used to predict secrecy-rate scaling without repeated numerical integration.

Where Pith is reading between the lines

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

  • The same bounding technique could be applied to other single-active-transmitter schemes such as index modulation in VLC.
  • If an active eavesdropper were present, the current bounds would no longer guarantee security and a different analysis would be required.
  • The performance ordering among selection schemes may change when the number of transmitters or the room geometry is altered.

Load-bearing premise

The eavesdropper is passive and its channel state is known or can be bounded, while the indoor VLC propagation follows the standard line-of-sight plus diffuse model used to compute mutual information.

What would settle it

In a controlled indoor VLC testbed, measure the empirical secrecy rate with a real passive eavesdropper whose channel differs from the modeled LOS-plus-diffuse statistics and check whether the measured value lies inside the derived lower and upper bounds.

Figures

Figures reproduced from arXiv: 1906.09512 by Hong Ge, Jianxin Dai, Jin-Yuan Wang, Jun-Bo Wang, Min Lin, Mohamed-Slim Alouini.

Figure 1
Figure 1. Figure 1: An indoor VLC network with Alice, Bob and Eve. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The diagram of the SM in VLC. At the current time instant, we suppose that the m-th LED is activated. Therefore, the received signals at Bob and Eve are given by ( YB = hB,mX + ZB YE = hE,mX + ZE , m = 1, 2, · · · , M, (1) where ZB ∼ N(0, σ2 B ) and ZE ∼ N(0, σ2 E ) are additive white Gaussian noises at Bob and Eve, σ 2 B and σ 2 E are the noise variances. hk,m is the direct current channel gain between th… view at source ↗
Figure 3
Figure 3. Figure 3: Secrecy rate bounds versus P with different hB/hE when ξ = 0.5. TABLE II PERFORMANCE GAPS BETWEEN (7) AND (15) WHEN ξ = 0.5. P (dB) Performance gaps (nat/transmission) hB = 10hE hB = 100hE hB = 1000hE 30 0.46736 0.46762 0.49213 40 0.46735 0.46736 0.46761 50 0.46735 0.46736 0.46736 60 0.46735 0.46736 0.46735 70 0.46735 0.46736 0.46735 80 0.46735 0.46736 0.46735 all the secrecy rate bounds increase first and… view at source ↗
Figure 4
Figure 4. Figure 4: Secrecy rate bounds versus ξ with different P when hB/hE = 1000. the increase of ξ. However, for large ξ, the secrecy rate bounds increase slowly and then tend to stable values as the increase of ξ. Moreover, with the increase of P, the secrecy rate performance also improves. This indicates that an indoor VLC system with larger nominal optical intensity has better performance [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 5
Figure 5. Figure 5: Secrecy rate bounds versus hB/hE with different P when ξ = 0.5. B. Results of SM Based VLC with Constraints (3), (4) and (5) [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Secrecy rate bounds versus P with different hB/hE when A = P. TABLE III PERFORMANCE GAPS BETWEEN (20) AND (22) WHEN A = P AND ξ = 0.5. P (dB) Performance gaps (nat/transmission) hB = 10hE hB = 100hE hB = 1000hE 30 0.17650 0.17672 0.19849 40 0.17649 0.17649 0.17672 50 0.17649 0.17649 0.17649 60 0.17649 0.17649 0.17649 70 0.17649 0.17649 0.17649 80 0.17649 0.17649 0.17649 TABLE IV PERFORMANCE GAPS BETWEEN (2… view at source ↗
Figure 7
Figure 7. Figure 7: Secrecy rare bounds versus ξ with different A when P = A and hB/hE = 1000. upper bounds of secrecy rate (22) always increase with the increase of ξ. Moreover, the larger the peak optical intensity A is, the slower the increasing trend of the upper bound (22) becomes. Furthermore, with the increase of A, the performance gaps between the lower and upper bounds of secrecy rate become smaller and smaller [PIT… view at source ↗
Figure 8
Figure 8. Figure 8: Secrecy rate bounds versus hB/hE with different A when ξ = 0.5 and A = P. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 1 2 3 4 5 6 7 8 Secrecy Rate (nat/transmission)  Upper bound, US Lower bound, US Upper bound, CAS Lower bound, CAS Upper bound, GS Lower bound, GS [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Average secrecy rate bounds versus ξ for three transmitter selection schemes when P = 25 dB and hB/hE = 1000. satisfying hB/hE = 1000. With the constraints (3) and (5), [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average secrecy rate bounds versus ξ for three transmitter selection schemes when A = P = 25 dB and hB/hE = 1000. system. The newly proposed GS and CAS schemes can provide large secrecy performance gains over the US scheme. When ξ is small, the performance gains of the GS and CAS schemes are dramatically. With the increase of ξ, such performance gains tend to diminish. With the constraints (3), (4) and (5… view at source ↗
read the original abstract

In this paper, we investigate the physical-layer security for a spatial modulation (SM) based indoor visible light communication (VLC) system, which includes multiple transmitters, a legitimate receiver, and a passive eavesdropper (Eve). At the transmitters, the SM scheme is employed, i.e., only one transmitter is active at each time instant. To choose the active transmitter, a uniform selection (US) scheme is utilized. Two scenarios are considered: one is with non-negativity and average optical intensity constraints, the other is with non-negativity, average optical intensity and peak optical intensity constraints. Then, lower and upper bounds on the secrecy rate are derived for these two scenarios. Besides, the asymptotic behaviors for the derived secrecy rate bounds at high signal-to-noise ratio (SNR) are analyzed. To further improve the secrecy performance, a channel adaptive selection (CAS) scheme and a greedy selection (GS) scheme are proposed to select the active transmitter. Numerical results show that the lower and upper bounds of the secrecy rate are tight. At high SNR, small asymptotic performance gaps exist between the derived lower and upper bounds. Moreover, the proposed GS scheme has the best performance, followed by the CAS scheme and the US scheme.

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

1 major / 2 minor

Summary. The paper derives lower and upper bounds on the secrecy rate of spatial modulation (SM) VLC systems with multiple transmitters under two optical intensity constraint sets (non-negativity + average; non-negativity + average + peak), analyzes high-SNR asymptotics, and proposes channel-adaptive selection (CAS) and greedy selection (GS) schemes that outperform uniform selection (US). Numerical results are presented to show that the bounds are tight and that GS yields the highest secrecy rate.

Significance. If the bounds are valid, the work supplies concrete analytical tools and selection heuristics for physical-layer secrecy in intensity-constrained SM-VLC, a setting of practical interest for indoor secure communications. The reported numerical tightness of the bounds and the consistent performance ordering among US/CAS/GS constitute verifiable strengths.

major comments (1)
  1. [System model / Secrecy rate bounds] System model and secrecy-rate derivation sections: the lower/upper bounds and the optimality claims for CAS/GS are obtained by direct substitution of Eve’s LOS+diffuse channel coefficients into the mutual-information expressions. For a passive Eve these coefficients are not known a priori at the transmitter; the manuscript does not state the precise assumption (worst-case Eve, statistical knowledge, or perfect CSI) under which the derived expressions remain valid secrecy-rate guarantees. This assumption is load-bearing for both the analytic bounds and the numerical superiority of GS.
minor comments (2)
  1. [Abstract] Abstract: the statement that “small asymptotic performance gaps exist” is not quantified; a sentence giving the observed gap values (or a reference to the relevant figure) would improve clarity.
  2. [Introduction / System model] Notation: the distinction between the two constraint scenarios is introduced only in the abstract and introduction; a single compact table summarizing the constraint sets and the corresponding bound expressions would aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the system model and the need to clarify assumptions regarding the eavesdropper's channel state information. We address this point below and will revise the manuscript to make the assumptions explicit.

read point-by-point responses

  1. Referee: [System model / Secrecy rate bounds] System model and secrecy-rate derivation sections: the lower/upper bounds and the optimality claims for CAS/GS are obtained by direct substitution of Eve’s LOS+diffuse channel coefficients into the mutual-information expressions. For a passive Eve these coefficients are not known a priori at the transmitter; the manuscript does not state the precise assumption (worst-case Eve, statistical knowledge, or perfect CSI) under which the derived expressions remain valid secrecy-rate guarantees. This assumption is load-bearing for both the analytic bounds and the numerical superiority of GS.

    Authors: We agree that the CSI assumption for Eve must be stated explicitly, as it is currently implicit. The secrecy-rate bounds are derived under the assumption of perfect knowledge of both the legitimate receiver's and Eve's channel coefficients at the transmitter. This corresponds to a worst-case Eve scenario for the purpose of computing the secrecy rate (i.e., the transmitter designs the scheme knowing Eve's LOS+diffuse coefficients). The CAS and GS schemes are likewise defined under this perfect-CSI assumption, as they select the active transmitter based on both channels. We will add a clear statement in the system model (Section II) and secrecy-rate derivation (Section III) specifying that the analysis assumes perfect CSI of Eve. Note that if only statistical CSI of Eve were available, the secrecy rate would instead be defined via ergodic or outage formulations, which is outside the scope of the current derivations but could be explored in future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bounds derived from standard mutual-information expressions

full rationale

The paper derives lower/upper secrecy-rate bounds and asymptotic high-SNR gaps directly from the standard secrecy-capacity formula (mutual information difference) under non-negativity, average-intensity, and (in one case) peak-intensity constraints for the SM transmitter selection schemes. These expressions are evaluated using the LOS+diffuse channel model for both Bob and Eve; the CAS/GS selection rules are explicit functions of the same channel coefficients. No step reduces a claimed prediction to a fitted parameter by construction, no uniqueness theorem is imported from prior self-work, and no ansatz is smuggled via citation. The derivation chain is therefore self-contained against external information-theoretic benchmarks and receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard information-theoretic definitions of secrecy rate and mutual information under non-negativity and intensity constraints; no free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • standard math Standard definitions of secrecy rate as difference of mutual informations
    Used to obtain lower and upper bounds on achievable secrecy rate
  • domain assumption Indoor VLC channel model with line-of-sight and diffuse components
    Implicit in the derivation of rate expressions for the legitimate and eavesdropper links

pith-pipeline@v0.9.0 · 5766 in / 1232 out tokens · 28504 ms · 2026-05-25T17:39:11.480775+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    What will 5G be?

    J. G. Andrews, S. Buzzi, W. Choi, S. V . Hanly, A. Lozano, A. C. K. Soong, and J. C. Zhang, “What will 5G be?” IEEE J. Sel. Areas Commun. , vol. 32, no. 6, pp. 1065-1082, Jun. 2014

    work page 2014

  2. [2]

    50 years of permutation, spatial and index modulation: From classic RF to visible light communications and data storage,

    N. Ishikawa, S. Sugiura, and L. Hanzo, “50 years of permutation, spatial and index modulation: From classic RF to visible light communications and data storage,” IEEE Commun. Surv. Tur ., vol. 20, no. 3, pp. 1905-1938, Mar. 2018

    work page 1905

  3. [3]

    Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,

    M. D. Renzo, H. Hass, A. Ghrayeb, S. Sugiura, and L. Hanzo, “Spatial modulation for generalized MIMO: Challenges, opportunities, and implementation,” Proc. IEEE, vol. 102, no. 1, pp. 56-103, Jan. 2014

    work page 2014

  4. [4]

    Space modulation on wireless fading channels,

    A. Chau and S.-H. Yu, “Space modulation on wireless fading channels,” in IEEE V eh. Technol. Conf., Atlantic City, USA, vol. 3, pp. 1668-1671, Oct. 2001

    work page 2001

  5. [5]

    Spatial modulation - A new low complexity spectral efficiency enhancing technique,

    R. Y . Mesleh, H. Haas, C. W. Ahn, and S. Yun, “Spatial modulation - A new low complexity spectral efficiency enhancing technique,” in Int. Conf. Commun. Netw. China , Beijing, China, pp. 1-5, Oct. 2006

    work page 2006

  6. [6]

    Spatial modulation,

    R. Y . Mesleh, H. Haas, S. Sinanovic, C. Ahn, and S. Yun, “Spatial modulation,” IEEE Trans. V eh. Technol., vol. 57, no. 4, pp. 2228-2241, Jul. 2008

    work page 2008

  7. [7]

    Spatial modulation: Optimal detection and performance analysis,

    J. Jeganathan, A. Ghrayeb, and L. Szczecinski, “Spatial modulation: Optimal detection and performance analysis,” IEEE Commun. Lett. , vol. 12, no. 8, pp. 545-547, Aug. 2008

    work page 2008

  8. [8]

    Detection algorithm for spatial modulation system under unconstrained channel,

    M. X. Guo, C. Jia, and Y . H. Shen, “Detection algorithm for spatial modulation system under unconstrained channel,” in IEEE Int. Conf. Commun. Technol. , Nanjing, China, pp. 458-461, Nov. 2010

    work page 2010

  9. [9]

    Generalised sphere decoding for spatial modulation,

    A. Younis, S. Sinanovic, M. Di Renzo, R. Y . Mesleh, and H. Haas, “Generalised sphere decoding for spatial modulation,” IEEE Trans. Commun. , vol. 61, no. 7, pp. 2805-2815, Jul. 2013

    work page 2013

  10. [10]

    A new low-complexity near-ML detection algorithm for spatial modulation,

    Q. Tang, Y . Xiao, P. Yang, Q. Yu, and S. Li, “A new low-complexity near-ML detection algorithm for spatial modulation,” IEEE Wirel. Commun. Lett. , vol. 2, no. 1, pp. 90-93, Feb. 2013

    work page 2013

  11. [11]

    Information-guided channel-hopping for high data rate wireless communication,

    Y . Yang and B. Jiao, “Information-guided channel-hopping for high data rate wireless communication,” IEEE Commun. Lett., vol. 12, no. 4, pp. 225-227, Apr. 2008

    work page 2008

  12. [12]

    Bit error probability of SM-MIMO over generalized fading channels,

    M. D. Renzo and H. Haas, “Bit error probability of SM-MIMO over generalized fading channels,” IEEE Trans. V eh. Technol., vol. 61, no. 3, pp. 1124-1144, Mar. 2012

    work page 2012

  13. [13]

    On the performance of full-duplex two-way relay channels with spatial modulation,

    J. Zhang, Q. Li, K. J. Kim, Y . Wang, X. Ge, and J. Zhang, “On the performance of full-duplex two-way relay channels with spatial modulation,” IEEE Trans. Commun. , vol. 64, no. 12, pp. 4966-4982, Dec. 2016

    work page 2016

  14. [14]

    Design guidelines for spatial modulation,

    P. Yang, M. D. Renzo, Y . Xiao, S. Li, and L. Hanzo, “Design guidelines for spatial modulation,” IEEE Commun. Surv. Tutor ., vol. 17, no. 1, pp. 6-25, First quarter 2015

    work page 2015

  15. [15]

    Optical spatial modulation,

    R. Mesleh, H. Elgala, and H. Haas, “Optical spatial modulation,” IEEE/OSA J. Opt. Commun. Netw. , vol. 3, no. 3, pp. 234-244, Mar. 2011

    work page 2011

  16. [16]

    Spatial modulation applied to optical wireless communications in indoor LOS environments,

    T. Fath, H. Haas, M. Di Renzo, and R. Mesleh, “Spatial modulation applied to optical wireless communications in indoor LOS environments,” in IEEE Global Telecommun. Conf. , Kathmandu, Nepal, pp. 1-5, Dec. 2011

    work page 2011

  17. [17]

    Performance comparison of MIMO techniques for optical wireless communications in indoor environments,

    T. Fath and H. Haas, “Performance comparison of MIMO techniques for optical wireless communications in indoor environments,” IEEE Trans. Commun. , vol. 61, no. 2, pp. 733-742, Feb. 2013

    work page 2013

  18. [18]

    Maximizing constrained capacity of power-imbalanced optical wireless MIMO communica- tions using spatial modulation,

    N. Ishikawa and S. Sugiura, “Maximizing constrained capacity of power-imbalanced optical wireless MIMO communica- tions using spatial modulation,” IEEE/OSA J. Lightwave Technol. , vol. 33, no. 2, pp. 519-527, Jan. 2015. 30

    work page 2015

  19. [19]

    On the performance of spatial modulation-based optical wireless communications,

    J.-Y . Wang, Z. Yang, Y . Wang, and M. Chen, “On the performance of spatial modulation-based optical wireless communications,” IEEE Photon. Technol. Lett. , vol. 28, no. 19, pp. 2094-2097, Oct. 2016

    work page 2094

  20. [20]

    Adaptive spatial modulation based visible light communications: SER analysis and optimization,

    J.-Y . Wang, J. Zhu, S. Lin, and J. Wang, “Adaptive spatial modulation based visible light communications: SER analysis and optimization,” IEEE Photon. J. , vol. 10, no. 3, pp. 1-14, Jun. 2018

    work page 2018

  21. [21]

    Channel-adapted spatial modulation for massive MIMO visible light communications,

    K. Xu, H. Yu, and Y .-J. Zhu, “Channel-adapted spatial modulation for massive MIMO visible light communications,” IEEE Photon. Technol. Lett. , vol. 28, no. 23, pp. 2693-2696, Dec. 2016

    work page 2016

  22. [22]

    Adaptive spatial modulation for visible light communications with an arbitrary number of transmitters,

    J.-Y . Wang, H. Ge, J.-X. Zhu, J.-B. Wang, J. Dai, and M. Lin, “Adaptive spatial modulation for visible light communications with an arbitrary number of transmitters,” IEEE Access , vol. 6, pp. 37108-37123, Jun. 2018

    work page 2018

  23. [23]

    Power efficient generalized spatial modulation MIMO for indoor visible light communications,

    C. R. Kumar and R. K. Jeyachitra, “Power efficient generalized spatial modulation MIMO for indoor visible light communications,” IEEE Photon. Techno. Lett. , vol. 29, no. 11, pp. 921-924, June 2017

    work page 2017

  24. [24]

    Effect of synchronization error on optical spatial modulation,

    H. G. Olanrewaju and W. O. Popoola, “Effect of synchronization error on optical spatial modulation,” IEEE Trans. Commun., vol. 65, no. 12, pp. 5362-5347, Dec. 2017

    work page 2017

  25. [25]

    Iterative combinatorial symbol design for spatial modulation in MIMO VLC systems,

    E. Curry and D. K. Borah, “Iterative combinatorial symbol design for spatial modulation in MIMO VLC systems,” IEEE Photon. Technol. Lett. , vol. 30, no. 5, pp. 483-486, Mar. 2018

    work page 2018

  26. [26]

    Physical-layer security for MISO visible light communication channels,

    A. Mostafa and L. Lampe, “Physical-layer security for MISO visible light communication channels,” IEEE J. Sel. Areas Commun., vol. 33, no. 9, pp. 1806-1818, Sep. 2015

    work page 2015

  27. [27]

    On the secrecy capacity of MISO visible light communication channels,

    M. A. Arfaoui, Z. Rezki, A. Ghrayeb, and M.-S. Alouini, “On the secrecy capacity of MISO visible light communication channels,” in IEEE Global Commun. Conf. , Washington, DC, USA, pp. 1-7, Dec. 2016

    work page 2016

  28. [28]

    Discrete input signaling for MISO visible light communication channels,

    M. A. Arfaoui, Z. Rezki, A. Ghrayeb, and M.-S. Alouini, “Discrete input signaling for MISO visible light communication channels,” in IEEE Wirel. Commun. Netw. Conf. , San Francisco, USA, pp. 1-6, Mar. 2017

    work page 2017

  29. [29]

    Physical-layer security for indoor visible light communications: Secrecy capacity analysis,

    J.-Y . Wang, C. Liu, J. Wang, Y . Wu, M. Lin and J. Cheng, “Physical-layer security for indoor visible light communications: Secrecy capacity analysis,” IEEE Trans. Commun. , Jul. 2018, DOI: 10.1109/TCOMM.2018.2859943

    work page doi:10.1109/tcomm.2018.2859943 2018

  30. [30]

    Secure hybrid VLC-RF systems with light energy harvesting,

    G. Pan, J. Ye, and Z. Ding, “Secure hybrid VLC-RF systems with light energy harvesting,” IEEE Trans. Commun. , vol. 65, no. 10, pp. 4348-4359, Oct. 2017

    work page 2017

  31. [31]

    On secure VLC systems with spatially random terminals,

    G. Pan, J. Ye, and Z. Ding, “On secure VLC systems with spatially random terminals,” IEEE Commun. Lett. , vol. 21, no. 3, pp. 492-495, Mar. 2017

    work page 2017

  32. [32]

    Fundamental analysis for visible-light communication system using LED lights,

    T. Komine and M. Nakagawa, “Fundamental analysis for visible-light communication system using LED lights,” IEEE Trans. Consum. Electron. , vol. 50, no. 1, pp. 100-107, Feb. 2004

    work page 2004

  33. [33]

    Tight bounds on channel capacity for dimmable visible light communications,

    J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y . Wang, “Tight bounds on channel capacity for dimmable visible light communications,” IEEE/OSA J. Lightwave Technol. , vol. 31, no. 23, pp. 3771-3779, Dec. 2013

    work page 2013

  34. [34]

    Elements of Information Theory ,

    T. M. Cover and J. A. Thomas, “ Elements of Information Theory ,” Hoboken, NJ, USA: Wiley, 2006

    work page 2006

  35. [35]

    Information Theory: Coding Theorems for Discrete Memoryless Systems ,

    I. Csiszar and J. Korner, “ Information Theory: Coding Theorems for Discrete Memoryless Systems ,” New York: Academic, 1981

    work page 1981

  36. [36]

    On the capacity of free-space optical intensity channels,

    A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory, vol. 55, no. 10, pp. 4449-4461, Oct. 2009

    work page 2009

  37. [37]

    Free-space optical communications: Capacity bounds, approximations, and a new sphere-packing perspective,

    A. Chaaban, J.-M. Morvan, and M.-S. Alouini, “Free-space optical communications: Capacity bounds, approximations, and a new sphere-packing perspective,” IEEE Trans. Commun. , vol. 64, no. 3, pp. 1176-1191, Mar. 2016

    work page 2016